import numpy as np
import pandas as pd
import seaborn as sns
from matplotlib import pyplot as plt
import warnings
warnings.filterwarnings('ignore')
sns.set()
from IPython.display import display
spdf = pd.read_csv("Sparkling.csv")
spdf.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 187 entries, 0 to 186 Data columns (total 2 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 YearMonth 187 non-null object 1 Sparkling 187 non-null int64 dtypes: int64(1), object(1) memory usage: 3.0+ KB
spdf.describe()
| Sparkling | |
|---|---|
| count | 187.000000 |
| mean | 2402.417112 |
| std | 1295.111540 |
| min | 1070.000000 |
| 25% | 1605.000000 |
| 50% | 1874.000000 |
| 75% | 2549.000000 |
| max | 7242.000000 |
spdf.head()
| YearMonth | Sparkling | |
|---|---|---|
| 0 | 1980-01 | 1686 |
| 1 | 1980-02 | 1591 |
| 2 | 1980-03 | 2304 |
| 3 | 1980-04 | 1712 |
| 4 | 1980-05 | 1471 |
spdf.tail()
| YearMonth | Sparkling | |
|---|---|---|
| 182 | 1995-03 | 1897 |
| 183 | 1995-04 | 1862 |
| 184 | 1995-05 | 1670 |
| 185 | 1995-06 | 1688 |
| 186 | 1995-07 | 2031 |
Date = pd.date_range(start="1980-01-01", periods=187, freq="M")
Date
DatetimeIndex(['1980-01-31', '1980-02-29', '1980-03-31', '1980-04-30',
'1980-05-31', '1980-06-30', '1980-07-31', '1980-08-31',
'1980-09-30', '1980-10-31',
...
'1994-10-31', '1994-11-30', '1994-12-31', '1995-01-31',
'1995-02-28', '1995-03-31', '1995-04-30', '1995-05-31',
'1995-06-30', '1995-07-31'],
dtype='datetime64[ns]', length=187, freq='M')
spdf["Date"] = Date
spdf.drop("YearMonth", axis=1, inplace=True)
spdf.set_index("Date", inplace=True)
spdf.head()
| Sparkling | |
|---|---|
| Date | |
| 1980-01-31 | 1686 |
| 1980-02-29 | 1591 |
| 1980-03-31 | 2304 |
| 1980-04-30 | 1712 |
| 1980-05-31 | 1471 |
spdf.index.freq = "M"
from pylab import rcParams # or we can write plt.rcParams['figure.figsize'] = 15,8
rcParams['figure.figsize'] = 15,8
spdf.plot()
plt.show()
sns.boxplot(x = spdf.index.year, y = spdf["Sparkling"])
plt.xlabel('Year')
plt.show()
sns.boxplot(x = spdf.index.month_name(), y = spdf["Sparkling"])
plt.xlabel('Month')
plt.show()
from statsmodels.graphics.tsaplots import month_plot
month_plot(spdf, ylabel="Sparkling Wine Sales")
from statsmodels.tsa.seasonal import seasonal_decompose
decomposition = seasonal_decompose(spdf, model="multiplicative")
decomposition.plot()
trend = decomposition.trend
seasonality = decomposition.seasonal
residual = decomposition.resid
print("Trend", "\n", trend.head(12), "\n")
print("Seasonality", "\n", seasonality.head(12), "\n")
print("Residual", "\n", residual.head(12), "\n")
Trend Date 1980-01-31 NaN 1980-02-29 NaN 1980-03-31 NaN 1980-04-30 NaN 1980-05-31 NaN 1980-06-30 NaN 1980-07-31 2360.666667 1980-08-31 2351.333333 1980-09-30 2320.541667 1980-10-31 2303.583333 1980-11-30 2302.041667 1980-12-31 2293.791667 Freq: M, Name: trend, dtype: float64 Seasonality Date 1980-01-31 0.649843 1980-02-29 0.659214 1980-03-31 0.757440 1980-04-30 0.730351 1980-05-31 0.660609 1980-06-30 0.603468 1980-07-31 0.809164 1980-08-31 0.918822 1980-09-30 0.894367 1980-10-31 1.241789 1980-11-30 1.690158 1980-12-31 2.384776 Freq: M, Name: seasonal, dtype: float64 Residual Date 1980-01-31 NaN 1980-02-29 NaN 1980-03-31 NaN 1980-04-30 NaN 1980-05-31 NaN 1980-06-30 NaN 1980-07-31 1.029230 1980-08-31 1.135407 1980-09-30 0.955954 1980-10-31 0.907513 1980-11-30 1.050423 1980-12-31 0.946770 Freq: M, Name: resid, dtype: float64
train = spdf[spdf.index.year < 1991]
test = spdf[spdf.index.year >= 1991]
train.shape, test.shape
((132, 1), (55, 1))
train["Sparkling"].plot(legend = True, label = "Train", fontsize = 14)
test["Sparkling"].plot(legend = True, label = "Test", fontsize = 14)
plt.show()
We are going to regress the "Sparkling" variable against the order of the occurrence. For this we need to modify our training data before fitting it into a linear regression.
train_time = [i + 1 for i in range(len(train))]
test_time = [i + 133 for i in range(len(test))]
print("Training time instance", "\n", train_time)
print("Test time instance", "\n", test_time)
print(len(train), len(test))
Training time instance [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132] Test time instance [133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187] 132 55
LinearRegression_train = train.copy()
LinearRegression_test = test.copy()
LinearRegression_train['time'] = train_time
LinearRegression_test['time'] = test_time
display(LinearRegression_train.head())
display(LinearRegression_train.tail())
| Sparkling | time | |
|---|---|---|
| Date | ||
| 1980-01-31 | 1686 | 1 |
| 1980-02-29 | 1591 | 2 |
| 1980-03-31 | 2304 | 3 |
| 1980-04-30 | 1712 | 4 |
| 1980-05-31 | 1471 | 5 |
| Sparkling | time | |
|---|---|---|
| Date | ||
| 1990-08-31 | 1605 | 128 |
| 1990-09-30 | 2424 | 129 |
| 1990-10-31 | 3116 | 130 |
| 1990-11-30 | 4286 | 131 |
| 1990-12-31 | 6047 | 132 |
from sklearn.linear_model import LinearRegression
lr = LinearRegression()
lr.fit(LinearRegression_train[["time"]], LinearRegression_train["Sparkling"])
LinearRegression()
test_predictions_model1 = lr.predict(LinearRegression_test[['time']])
LinearRegression_test['RegOnTime'] = test_predictions_model1
LinearRegression_test.head(12)
| Sparkling | time | RegOnTime | |
|---|---|---|---|
| Date | |||
| 1991-01-31 | 1902 | 133 | 2791.652093 |
| 1991-02-28 | 2049 | 134 | 2797.484752 |
| 1991-03-31 | 1874 | 135 | 2803.317410 |
| 1991-04-30 | 1279 | 136 | 2809.150069 |
| 1991-05-31 | 1432 | 137 | 2814.982727 |
| 1991-06-30 | 1540 | 138 | 2820.815386 |
| 1991-07-31 | 2214 | 139 | 2826.648044 |
| 1991-08-31 | 1857 | 140 | 2832.480703 |
| 1991-09-30 | 2408 | 141 | 2838.313361 |
| 1991-10-31 | 3252 | 142 | 2844.146020 |
| 1991-11-30 | 3627 | 143 | 2849.978678 |
| 1991-12-31 | 6153 | 144 | 2855.811337 |
Plot
train["Sparkling"].plot(legend = True, label = 'Train')
test["Sparkling"].plot(legend = True, label = 'Test')
LinearRegression_test['RegOnTime'].plot(legend = True, label = 'Test Preds using Linear Regression')
plt.show()
Accuracy Metrics
from statsmodels.tools.eval_measures import rmse
rmse_model1_test = rmse(test["Sparkling"], test_predictions_model1)
rmse_model1_test
1389.135174897992
resultsDf = pd.DataFrame({"Test RMSE": [rmse_model1_test]}, index = ["RegressionOnTime"])
resultsDf
| Test RMSE | |
|---|---|
| RegressionOnTime | 1389.135175 |
NaiveModel_train = train.copy()
NaiveModel_test = test.copy()
NaiveModel_test["naive"] = train["Sparkling"][len(train["Sparkling"])-1]
NaiveModel_test["naive"].head()
Date 1991-01-31 6047 1991-02-28 6047 1991-03-31 6047 1991-04-30 6047 1991-05-31 6047 Freq: M, Name: naive, dtype: int64
train["Sparkling"].plot(legend = True, label = "Train")
test["Sparkling"].plot(legend = True, label = "Test")
NaiveModel_test["naive"].plot(legend = True, label = "Naive Model Test Preds")
plt.show()
Model Evaluation
rmse_model2_test = rmse(test["Sparkling"], NaiveModel_test["naive"])
print("RMSE for Naive Bayes",rmse_model2_test)
resultsDf_2 = pd.DataFrame({"Test RMSE": [rmse_model2_test]}, index=["NaiveModel"])
resultsDf = pd.concat([resultsDf, resultsDf_2])
display(resultsDf)
RMSE for Naive Bayes 3864.2793518443914
| Test RMSE | |
|---|---|
| RegressionOnTime | 1389.135175 |
| NaiveModel | 3864.279352 |
SimpleAverage_train = train.copy()
SimpleAverage_test = test.copy()
SimpleAverage_test["mean_Sparkling"] = train["Sparkling"].mean()
SimpleAverage_test.head()
| Sparkling | mean_Sparkling | |
|---|---|---|
| Date | ||
| 1991-01-31 | 1902 | 2403.780303 |
| 1991-02-28 | 2049 | 2403.780303 |
| 1991-03-31 | 1874 | 2403.780303 |
| 1991-04-30 | 1279 | 2403.780303 |
| 1991-05-31 | 1432 | 2403.780303 |
train["Sparkling"].plot(legend = True, label = "Train")
test["Sparkling"].plot(legend = True, label = "Test")
SimpleAverage_test["mean_Sparkling"].plot(legend = True, label = "Simple Avg Test Predictions")
plt.show()
Model Evaluation
rmse_model3_test = rmse(test["Sparkling"], SimpleAverage_test["mean_Sparkling"])
print("RMSE for Simple Average Model is", rmse_model3_test)
RMSE for Simple Average Model is 1275.0818036965309
reultsDf_3 = pd.DataFrame({"Test RMSE": [rmse_model3_test]}, index = ["SimpleAverageModel"])
resultsDf = pd.concat([resultsDf, reultsDf_3])
resultsDf
| Test RMSE | |
|---|---|
| RegressionOnTime | 1389.135175 |
| NaiveModel | 3864.279352 |
| SimpleAverageModel | 1275.081804 |
For the moving average model, we are going to calculate rolling means (or moving averages) for different intervals. The best interval can be determined by the maximum accuracy (or the minimum error) over here.
For Moving Average, we are going to average over the entire data.
MovingAverage = spdf.copy()
MovingAverage.head()
| Sparkling | |
|---|---|
| Date | |
| 1980-01-31 | 1686 |
| 1980-02-29 | 1591 |
| 1980-03-31 | 2304 |
| 1980-04-30 | 1712 |
| 1980-05-31 | 1471 |
Trailing moving averages
MovingAverage["Trailing_2"] = MovingAverage["Sparkling"].rolling(2).mean()
MovingAverage["Trailing_4"] = MovingAverage["Sparkling"].rolling(4).mean()
MovingAverage["Trailing_6"] = MovingAverage["Sparkling"].rolling(6).mean()
MovingAverage["Trailing_9"] = MovingAverage["Sparkling"].rolling(9).mean()
MovingAverage.head()
| Sparkling | Trailing_2 | Trailing_4 | Trailing_6 | Trailing_9 | |
|---|---|---|---|---|---|
| Date | |||||
| 1980-01-31 | 1686 | NaN | NaN | NaN | NaN |
| 1980-02-29 | 1591 | 1638.5 | NaN | NaN | NaN |
| 1980-03-31 | 2304 | 1947.5 | NaN | NaN | NaN |
| 1980-04-30 | 1712 | 2008.0 | 1823.25 | NaN | NaN |
| 1980-05-31 | 1471 | 1591.5 | 1769.50 | NaN | NaN |
Plot the data
plt.figure(figsize=(16,8))
plt.plot(MovingAverage["Sparkling"], label="Train")
plt.plot(MovingAverage["Trailing_2"], label="2 point Moving Average")
plt.plot(MovingAverage["Trailing_4"], label="4 point Moving Average")
plt.plot(MovingAverage["Trailing_6"], label="6 point Moving Average")
plt.plot(MovingAverage["Trailing_9"], label="9 point Moving Average")
plt.legend(loc="best")
plt.grid()
plt.show()
Split the data into train and test and plot
trailing_MovingAverage_train = MovingAverage[MovingAverage.index.year < 1991]
trailing_MovingAverage_test = MovingAverage[MovingAverage.index.year >= 1991]
plt.figure(figsize=(16,8))
plt.plot(trailing_MovingAverage_train["Sparkling"], label="Train")
plt.plot(trailing_MovingAverage_test["Sparkling"], label="Test")
plt.plot(trailing_MovingAverage_train["Trailing_2"], label="2 point Trailing Moving Average on Training Set")
plt.plot(trailing_MovingAverage_train["Trailing_4"], label="4 point Trailing Moving Average on Training Set")
plt.plot(trailing_MovingAverage_train["Trailing_6"], label="6 point Trailing Moving Average on Training Set")
plt.plot(trailing_MovingAverage_train["Trailing_9"], label="9 point Trailing Moving Average on Training Set")
plt.plot(trailing_MovingAverage_test["Trailing_2"], label="2 point Trailing Moving Average on Test Set")
plt.plot(trailing_MovingAverage_test["Trailing_4"], label="4 point Trailing Moving Average on Test Set")
plt.plot(trailing_MovingAverage_test["Trailing_6"], label="6 point Trailing Moving Average on Test Set")
plt.plot(trailing_MovingAverage_test["Trailing_9"], label="9 point Trailing Moving Average on Test Set")
plt.legend(loc="best")
plt.grid()
plt.show()
Model Evaluation
rmse_model4_test_2 = rmse(test["Sparkling"], trailing_MovingAverage_test["Trailing_2"])
print("Rmse for trailing_2", rmse_model4_test_2)
rmse_model4_test_4 = rmse(test["Sparkling"], trailing_MovingAverage_test["Trailing_4"])
print("Rmse for trailing_4", rmse_model4_test_4)
rmse_model4_test_6 = rmse(test["Sparkling"], trailing_MovingAverage_test["Trailing_6"])
print("Rmse for trailing_6", rmse_model4_test_6)
rmse_model4_test_9 = rmse(test["Sparkling"], trailing_MovingAverage_test["Trailing_9"])
print("Rmse for trailing_9", rmse_model4_test_9)
resultsDf_4 = pd.DataFrame({"Test RMSE": [rmse_model4_test_2, rmse_model4_test_4, rmse_model4_test_6, rmse_model4_test_9]},
index = ["2_point_trailing_Moving_Average", "4_point_trailing_Moving_Average", "6_point_trailing_Moving_Average", "9_point_trailing_Moving_Average"])
resultsDf = pd.concat([resultsDf, resultsDf_4])
resultsDf
Rmse for trailing_2 813.4006839972983 Rmse for trailing_4 1156.589694081071 Rmse for trailing_6 1283.9274280129855 Rmse for trailing_9 1346.2783154241804
| Test RMSE | |
|---|---|
| RegressionOnTime | 1389.135175 |
| NaiveModel | 3864.279352 |
| SimpleAverageModel | 1275.081804 |
| 2_point_trailing_Moving_Average | 813.400684 |
| 4_point_trailing_Moving_Average | 1156.589694 |
| 6_point_trailing_Moving_Average | 1283.927428 |
| 9_point_trailing_Moving_Average | 1346.278315 |
Plot of all models derived till now
train["Sparkling"].plot(legend=True, label="Train")
test["Sparkling"].plot(legend=True, label="Test")
LinearRegression_test["RegOnTime"].plot(legend=True, label="Test Preds using Linear Regression")
NaiveModel_test["naive"].plot(legend=True, label="Naive Model Test Preds")
SimpleAverage_test["mean_Sparkling"].plot(legend=True, label="Simple Avg Test Preds")
trailing_MovingAverage_test["Trailing_2"].plot(legend=True, label="Trailing MA 2 test preds")
plt.show()
from statsmodels.tsa.api import ExponentialSmoothing, SimpleExpSmoothing, Holt
SES_train = train.copy()
SES_test = test.copy()
model_SES = SimpleExpSmoothing(SES_train["Sparkling"]);
model_SES_autofit = model_SES.fit()
display("SES Params", model_SES_autofit.params)
SES_test["predict"] = model_SES_autofit.forecast(steps=len(test))
display(SES_test.head().style)
SES_train["Sparkling"].plot(legend=True, label="Train")
SES_test["Sparkling"].plot(legend=True, label="Test")
SES_test["predict"].plot(legend=True, label="SES Preds on Test")
plt.show()
C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn(
'SES Params'
{'smoothing_level': 0.04960736049406556,
'smoothing_trend': nan,
'smoothing_seasonal': nan,
'damping_trend': nan,
'initial_level': 2151.614314422547,
'initial_trend': nan,
'initial_seasons': array([], dtype=float64),
'use_boxcox': False,
'lamda': None,
'remove_bias': False}
| Sparkling | predict | |
|---|---|---|
| Date | ||
| 1991-01-31 00:00:00 | 1902 | 2725.336037 |
| 1991-02-28 00:00:00 | 2049 | 2725.336037 |
| 1991-03-31 00:00:00 | 1874 | 2725.336037 |
| 1991-04-30 00:00:00 | 1279 | 2725.336037 |
| 1991-05-31 00:00:00 | 1432 | 2725.336037 |
rmse_model5_test_1 = rmse(SES_test["Sparkling"], SES_test["predict"])
display(rmse_model5_test_1)
resultsDf_5 = pd.DataFrame({"Test RMSE": [rmse_model5_test_1]}, index=["Alpha=0.03,SimpleExponentialSmoothing"])
resultsDf = pd.concat([resultsDf, resultsDf_5])
display(resultsDf)
1316.1354111921867
| Test RMSE | |
|---|---|
| RegressionOnTime | 1389.135175 |
| NaiveModel | 3864.279352 |
| SimpleAverageModel | 1275.081804 |
| 2_point_trailing_Moving_Average | 813.400684 |
| 4_point_trailing_Moving_Average | 1156.589694 |
| 6_point_trailing_Moving_Average | 1283.927428 |
| 9_point_trailing_Moving_Average | 1346.278315 |
| Alpha=0.03,SimpleExponentialSmoothing | 1316.135411 |
resultsDf_6 = pd.DataFrame({"Alpha Values":[], "Train RMSE": [], "Test RMSE": []})
alpha_list = [0.3,0.4,0.5,0.6,0.7,0.8,0.9]
for i in alpha_list:
model_SES_alpha_i = model_SES.fit(smoothing_level=i)
SES_train["predict",i] = model_SES_alpha_i.fittedvalues
SES_test["predict",i] = model_SES_alpha_i.forecast(steps=len(test))
rmse_model5_train_i = rmse(SES_train["Sparkling"],SES_train["predict",i])
rmse_model5_test_i = rmse(SES_test["Sparkling"],SES_test["predict",i])
resultsDf_6 = resultsDf_6.append({"Alpha Values":i,
"Train RMSE": rmse_model5_train_i,"Test RMSE":rmse_model5_test_i},
ignore_index=True)
display(SES_test.head().style)
display("Model Evaluation", resultsDf_6.sort_values(by=["Test RMSE"],ascending=True))
| Sparkling | predict | ('predict', 0.3) | ('predict', 0.4) | ('predict', 0.5) | ('predict', 0.6) | ('predict', 0.7) | ('predict', 0.8) | ('predict', 0.9) | |
|---|---|---|---|---|---|---|---|---|---|
| Date | |||||||||
| 1991-01-31 00:00:00 | 1902 | 2725.336037 | 3855.296454 | 4327.657882 | 4740.858018 | 5091.699384 | 5388.514029 | 5641.221537 | 5858.428614 |
| 1991-02-28 00:00:00 | 2049 | 2725.336037 | 3855.296454 | 4327.657882 | 4740.858018 | 5091.699384 | 5388.514029 | 5641.221537 | 5858.428614 |
| 1991-03-31 00:00:00 | 1874 | 2725.336037 | 3855.296454 | 4327.657882 | 4740.858018 | 5091.699384 | 5388.514029 | 5641.221537 | 5858.428614 |
| 1991-04-30 00:00:00 | 1279 | 2725.336037 | 3855.296454 | 4327.657882 | 4740.858018 | 5091.699384 | 5388.514029 | 5641.221537 | 5858.428614 |
| 1991-05-31 00:00:00 | 1432 | 2725.336037 | 3855.296454 | 4327.657882 | 4740.858018 | 5091.699384 | 5388.514029 | 5641.221537 | 5858.428614 |
'Model Evaluation'
| Alpha Values | Train RMSE | Test RMSE | |
|---|---|---|---|
| 0 | 0.3 | 1359.422161 | 1935.507132 |
| 1 | 0.4 | 1352.562367 | 2311.919615 |
| 2 | 0.5 | 1343.994119 | 2666.351413 |
| 3 | 0.6 | 1338.801426 | 2979.204388 |
| 4 | 0.7 | 1338.843297 | 3249.944092 |
| 5 | 0.8 | 1344.462034 | 3483.801006 |
| 6 | 0.9 | 1355.723496 | 3686.794285 |
plt.figure(figsize=(18,9))
plt.plot(SES_train["Sparkling"], label="Train")
plt.plot(SES_test["Sparkling"], label="Test")
plt.plot(SES_test["predict"], label="Alpha=1 Simple Exponential Smoothing predictions on Test Set")
plt.plot(SES_test["predict", 0.4], label="Alpha=0.4 Simple Exponential Smoothing predictions on Test Set")
plt.legend(loc="best")
plt.grid()
plt.show()
resultsDf_6_1 = pd.DataFrame({"Test RMSE": [resultsDf_6.sort_values(by=["Test RMSE"], ascending=True).values[0][2]]},
index = ["Alpha=0.4,SimpleExponentialSmoothing"])
resultsDf = pd.concat([resultsDf, resultsDf_6_1])
display(resultsDf.style)
| Test RMSE | |
|---|---|
| RegressionOnTime | 1389.135175 |
| NaiveModel | 3864.279352 |
| SimpleAverageModel | 1275.081804 |
| 2_point_trailing_Moving_Average | 813.400684 |
| 4_point_trailing_Moving_Average | 1156.589694 |
| 6_point_trailing_Moving_Average | 1283.927428 |
| 9_point_trailing_Moving_Average | 1346.278315 |
| Alpha=0.03,SimpleExponentialSmoothing | 1316.135411 |
| Alpha=0.4,SimpleExponentialSmoothing | 1935.507132 |
DES_train = train.copy()
DES_test = test.copy()
model_DES = Holt(DES_train["Sparkling"])
resultsDf_7 = pd.DataFrame({"Alpha Values": [], "Beta Values": [], "Train RMSE": [], "Test RMSE": []})
alpha_list = [0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0]
beta_list = [0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0]
for i in alpha_list:
for j in beta_list:
model_DES_alpha_i_j = model_DES.fit(smoothing_level=i,smoothing_trend=j)
DES_train["predict",i,j] = model_DES_alpha_i_j.fittedvalues
DES_test["predict",i,j] = model_DES_alpha_i_j.forecast(steps=len(test))
rmse_model6_train = rmse(DES_train["Sparkling"],DES_train["predict",i,j])
rmse_model6_test = rmse(DES_test["Sparkling"],DES_test["predict",i,j])
resultsDf_7 = resultsDf_7.append({"Alpha Values":i,
"Beta Values":j,
"Train RMSE": rmse_model6_train,
"Test RMSE": rmse_model6_test}, ignore_index=True)
display(resultsDf_7.sort_values(by=["Test RMSE"]).head(10))
| Alpha Values | Beta Values | Train RMSE | Test RMSE | |
|---|---|---|---|---|
| 0 | 0.3 | 0.3 | 1590.151685 | 18259.110704 |
| 8 | 0.4 | 0.3 | 1568.527728 | 23878.496940 |
| 1 | 0.3 | 0.4 | 1680.813420 | 26069.841401 |
| 16 | 0.5 | 0.3 | 1530.223975 | 27095.532414 |
| 24 | 0.6 | 0.3 | 1506.223118 | 29070.722592 |
| 32 | 0.7 | 0.3 | 1500.508563 | 30524.407568 |
| 40 | 0.8 | 0.3 | 1508.999847 | 31689.588069 |
| 9 | 0.4 | 0.4 | 1631.598723 | 32084.192549 |
| 48 | 0.9 | 0.3 | 1528.779355 | 32650.778085 |
| 56 | 1.0 | 0.3 | 1559.937648 | 33462.024859 |
plt.figure(figsize=(18,9))
plt.plot(DES_train["Sparkling"], label="Train")
plt.plot(DES_test["Sparkling"], label="Test")
plt.plot(DES_test["predict", 0.3, 0.3], label="Alpha=0.3,Beta=0.3,DoubleExponentialSmoothing predictions on Test Set")
plt.legend(loc="best")
plt.grid()
plt.show()
resultsDf_7_1 = pd.DataFrame({"Test RMSE": [resultsDf_7.sort_values(by=["Test RMSE"]).values[0][3]]}, index=["Alpha=0.3,Beta=0.3,DoubleExponentialSmoothing"])
resultsDf = pd.concat([resultsDf, resultsDf_7_1])
display(resultsDf)
| Test RMSE | |
|---|---|
| RegressionOnTime | 1389.135175 |
| NaiveModel | 3864.279352 |
| SimpleAverageModel | 1275.081804 |
| 2_point_trailing_Moving_Average | 813.400684 |
| 4_point_trailing_Moving_Average | 1156.589694 |
| 6_point_trailing_Moving_Average | 1283.927428 |
| 9_point_trailing_Moving_Average | 1346.278315 |
| Alpha=0.03,SimpleExponentialSmoothing | 1316.135411 |
| Alpha=0.4,SimpleExponentialSmoothing | 1935.507132 |
| Alpha=0.3,Beta=0.3,DoubleExponentialSmoothing | 18259.110704 |
TES_train = train.copy()
TES_test = test.copy()
model_TES = ExponentialSmoothing(TES_train["Sparkling"], trend="additive", seasonal="multiplicative", freq="M")
model_TES_autofit = model_TES.fit()
display(model_TES_autofit.params)
TES_test["auto_predict"] = model_TES_autofit.forecast(steps=len(test)).round(0)
display(TES_test.head())
plt.figure(figsize=(18,9))
plt.plot(TES_train["Sparkling"], label="Train")
plt.plot(TES_test["Sparkling"], label="Test")
plt.plot(TES_test["auto_predict"], label="Alpha=0.146,Beta=0.053,Gamma=0.393,TripleExponentialSmoothing")
plt.legend(loc="best")
plt.title("Plot with Autofit")
plt.grid()
plt.show()
{'smoothing_level': 0.11108840858679117,
'smoothing_trend': 0.061712060020663685,
'smoothing_seasonal': 0.3950814802151603,
'damping_trend': nan,
'initial_level': 1639.9088356475902,
'initial_trend': -11.928143593549056,
'initial_seasons': array([1.05065032, 1.02086214, 1.41078482, 1.20263518, 0.97315225,
0.96689379, 1.31724304, 1.70471609, 1.37289733, 1.81035002,
2.83962708, 3.60997333]),
'use_boxcox': False,
'lamda': None,
'remove_bias': False}
| Sparkling | auto_predict | |
|---|---|---|
| Date | ||
| 1991-01-31 | 1902 | 1577.0 |
| 1991-02-28 | 2049 | 1334.0 |
| 1991-03-31 | 1874 | 1746.0 |
| 1991-04-30 | 1279 | 1630.0 |
| 1991-05-31 | 1432 | 1523.0 |
rmse_model6_test_1 = rmse(TES_test["Sparkling"], TES_test["auto_predict"])
display(rmse_model6_test_1)
resultsDf_8_1 = pd.DataFrame({"Test RMSE": [rmse_model6_test_1]}, index=["Alpha=0.146,Beta=0.053,Gamma=0.393,TripleExponentialSmoothing"])
resultsDf = pd.concat([resultsDf, resultsDf_8_1])
display(resultsDf)
469.65604435586687
| Test RMSE | |
|---|---|
| RegressionOnTime | 1389.135175 |
| NaiveModel | 3864.279352 |
| SimpleAverageModel | 1275.081804 |
| 2_point_trailing_Moving_Average | 813.400684 |
| 4_point_trailing_Moving_Average | 1156.589694 |
| 6_point_trailing_Moving_Average | 1283.927428 |
| 9_point_trailing_Moving_Average | 1346.278315 |
| Alpha=0.03,SimpleExponentialSmoothing | 1316.135411 |
| Alpha=0.4,SimpleExponentialSmoothing | 1935.507132 |
| Alpha=0.3,Beta=0.3,DoubleExponentialSmoothing | 18259.110704 |
| Alpha=0.146,Beta=0.053,Gamma=0.393,TripleExponentialSmoothing | 469.656044 |
resultsDf_8_2 = pd.DataFrame({"Alpha Values":[],"Beta Values":[],"Gamma Values":[],"Train RMSE":[],"Test RMSE": []})
gamma_list = [0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0]
for i in alpha_list:
for j in beta_list:
for k in gamma_list:
model_TES_alpha_i_j_k = model_TES.fit(smoothing_level=i,
smoothing_trend=j,
smoothing_seasonal=k)
TES_train["predict",i,j,k] = model_TES_alpha_i_j_k.fittedvalues
TES_test["predict",i,j,k] = model_TES_alpha_i_j_k.forecast(steps=len(test))
rmse_model8_train = rmse(TES_train["Sparkling"],
TES_train["predict",i,j,k])
rmse_model8_test = rmse(TES_test["Sparkling"],
TES_test["predict",i,j,k])
resultsDf_8_2 = resultsDf_8_2.append({"Alpha Values":i,
"Beta Values":j,
"Gamma Values":k,
"Train RMSE":rmse_model8_train,
"Test RMSE":rmse_model8_test},ignore_index=True)
display(TES_test.head().style)
display(resultsDf_8_2.sort_values(by=["Test RMSE"]).head())
resultsDf_8_3 = pd.DataFrame({"Test RMSE": [resultsDf_8_2.sort_values(by=["Test RMSE"]).values[0][4]]}
,index=["Alpha=0.7,Beta=0.3,Gamma=0.3,TripleExponentialSmoothing"])
resultsDf = pd.concat([resultsDf, resultsDf_8_3])
display(resultsDf.sort_values(by=["Test RMSE"]))
C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn( C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\tsa\holtwinters\model.py:920: ConvergenceWarning: Optimization failed to converge. Check mle_retvals. warnings.warn(
| Sparkling | auto_predict | ('predict', 0.3, 0.3, 0.3) | ('predict', 0.3, 0.3, 0.4) | ('predict', 0.3, 0.3, 0.5) | ('predict', 0.3, 0.3, 0.6) | ('predict', 0.3, 0.3, 0.7) | ('predict', 0.3, 0.3, 0.8) | ('predict', 0.3, 0.3, 0.9) | ('predict', 0.3, 0.3, 1.0) | ('predict', 0.3, 0.4, 0.3) | ('predict', 0.3, 0.4, 0.4) | ('predict', 0.3, 0.4, 0.5) | ('predict', 0.3, 0.4, 0.6) | ('predict', 0.3, 0.4, 0.7) | ('predict', 0.3, 0.4, 0.8) | ('predict', 0.3, 0.4, 0.9) | ('predict', 0.3, 0.4, 1.0) | ('predict', 0.3, 0.5, 0.3) | ('predict', 0.3, 0.5, 0.4) | ('predict', 0.3, 0.5, 0.5) | ('predict', 0.3, 0.5, 0.6) | ('predict', 0.3, 0.5, 0.7) | ('predict', 0.3, 0.5, 0.8) | ('predict', 0.3, 0.5, 0.9) | ('predict', 0.3, 0.5, 1.0) | ('predict', 0.3, 0.6, 0.3) | ('predict', 0.3, 0.6, 0.4) | ('predict', 0.3, 0.6, 0.5) | ('predict', 0.3, 0.6, 0.6) | ('predict', 0.3, 0.6, 0.7) | ('predict', 0.3, 0.6, 0.8) | ('predict', 0.3, 0.6, 0.9) | ('predict', 0.3, 0.6, 1.0) | ('predict', 0.3, 0.7, 0.3) | ('predict', 0.3, 0.7, 0.4) | ('predict', 0.3, 0.7, 0.5) | ('predict', 0.3, 0.7, 0.6) | ('predict', 0.3, 0.7, 0.7) | ('predict', 0.3, 0.7, 0.8) | ('predict', 0.3, 0.7, 0.9) | ('predict', 0.3, 0.7, 1.0) | ('predict', 0.3, 0.8, 0.3) | ('predict', 0.3, 0.8, 0.4) | ('predict', 0.3, 0.8, 0.5) | ('predict', 0.3, 0.8, 0.6) | ('predict', 0.3, 0.8, 0.7) | ('predict', 0.3, 0.8, 0.8) | ('predict', 0.3, 0.8, 0.9) | ('predict', 0.3, 0.8, 1.0) | ('predict', 0.3, 0.9, 0.3) | ('predict', 0.3, 0.9, 0.4) | ('predict', 0.3, 0.9, 0.5) | ('predict', 0.3, 0.9, 0.6) | ('predict', 0.3, 0.9, 0.7) | ('predict', 0.3, 0.9, 0.8) | ('predict', 0.3, 0.9, 0.9) | ('predict', 0.3, 0.9, 1.0) | ('predict', 0.3, 1.0, 0.3) | ('predict', 0.3, 1.0, 0.4) | ('predict', 0.3, 1.0, 0.5) | ('predict', 0.3, 1.0, 0.6) | ('predict', 0.3, 1.0, 0.7) | ('predict', 0.3, 1.0, 0.8) | ('predict', 0.3, 1.0, 0.9) | ('predict', 0.3, 1.0, 1.0) | ('predict', 0.4, 0.3, 0.3) | ('predict', 0.4, 0.3, 0.4) | ('predict', 0.4, 0.3, 0.5) | ('predict', 0.4, 0.3, 0.6) | ('predict', 0.4, 0.3, 0.7) | ('predict', 0.4, 0.3, 0.8) | ('predict', 0.4, 0.3, 0.9) | ('predict', 0.4, 0.3, 1.0) | ('predict', 0.4, 0.4, 0.3) | ('predict', 0.4, 0.4, 0.4) | ('predict', 0.4, 0.4, 0.5) | ('predict', 0.4, 0.4, 0.6) | ('predict', 0.4, 0.4, 0.7) | ('predict', 0.4, 0.4, 0.8) | ('predict', 0.4, 0.4, 0.9) | ('predict', 0.4, 0.4, 1.0) | ('predict', 0.4, 0.5, 0.3) | ('predict', 0.4, 0.5, 0.4) | ('predict', 0.4, 0.5, 0.5) | ('predict', 0.4, 0.5, 0.6) | ('predict', 0.4, 0.5, 0.7) | ('predict', 0.4, 0.5, 0.8) | ('predict', 0.4, 0.5, 0.9) | ('predict', 0.4, 0.5, 1.0) | ('predict', 0.4, 0.6, 0.3) | ('predict', 0.4, 0.6, 0.4) | ('predict', 0.4, 0.6, 0.5) | ('predict', 0.4, 0.6, 0.6) | ('predict', 0.4, 0.6, 0.7) | ('predict', 0.4, 0.6, 0.8) | ('predict', 0.4, 0.6, 0.9) | ('predict', 0.4, 0.6, 1.0) | ('predict', 0.4, 0.7, 0.3) | ('predict', 0.4, 0.7, 0.4) | ('predict', 0.4, 0.7, 0.5) | ('predict', 0.4, 0.7, 0.6) | ('predict', 0.4, 0.7, 0.7) | ('predict', 0.4, 0.7, 0.8) | ('predict', 0.4, 0.7, 0.9) | ('predict', 0.4, 0.7, 1.0) | ('predict', 0.4, 0.8, 0.3) | ('predict', 0.4, 0.8, 0.4) | ('predict', 0.4, 0.8, 0.5) | ('predict', 0.4, 0.8, 0.6) | ('predict', 0.4, 0.8, 0.7) | ('predict', 0.4, 0.8, 0.8) | ('predict', 0.4, 0.8, 0.9) | ('predict', 0.4, 0.8, 1.0) | ('predict', 0.4, 0.9, 0.3) | ('predict', 0.4, 0.9, 0.4) | ('predict', 0.4, 0.9, 0.5) | ('predict', 0.4, 0.9, 0.6) | ('predict', 0.4, 0.9, 0.7) | ('predict', 0.4, 0.9, 0.8) | ('predict', 0.4, 0.9, 0.9) | ('predict', 0.4, 0.9, 1.0) | ('predict', 0.4, 1.0, 0.3) | ('predict', 0.4, 1.0, 0.4) | ('predict', 0.4, 1.0, 0.5) | ('predict', 0.4, 1.0, 0.6) | ('predict', 0.4, 1.0, 0.7) | ('predict', 0.4, 1.0, 0.8) | ('predict', 0.4, 1.0, 0.9) | ('predict', 0.4, 1.0, 1.0) | ('predict', 0.5, 0.3, 0.3) | ('predict', 0.5, 0.3, 0.4) | ('predict', 0.5, 0.3, 0.5) | ('predict', 0.5, 0.3, 0.6) | ('predict', 0.5, 0.3, 0.7) | ('predict', 0.5, 0.3, 0.8) | ('predict', 0.5, 0.3, 0.9) | ('predict', 0.5, 0.3, 1.0) | ('predict', 0.5, 0.4, 0.3) | ('predict', 0.5, 0.4, 0.4) | ('predict', 0.5, 0.4, 0.5) | ('predict', 0.5, 0.4, 0.6) | ('predict', 0.5, 0.4, 0.7) | ('predict', 0.5, 0.4, 0.8) | ('predict', 0.5, 0.4, 0.9) | ('predict', 0.5, 0.4, 1.0) | ('predict', 0.5, 0.5, 0.3) | ('predict', 0.5, 0.5, 0.4) | ('predict', 0.5, 0.5, 0.5) | ('predict', 0.5, 0.5, 0.6) | ('predict', 0.5, 0.5, 0.7) | ('predict', 0.5, 0.5, 0.8) | ('predict', 0.5, 0.5, 0.9) | ('predict', 0.5, 0.5, 1.0) | ('predict', 0.5, 0.6, 0.3) | ('predict', 0.5, 0.6, 0.4) | ('predict', 0.5, 0.6, 0.5) | ('predict', 0.5, 0.6, 0.6) | ('predict', 0.5, 0.6, 0.7) | ('predict', 0.5, 0.6, 0.8) | ('predict', 0.5, 0.6, 0.9) | ('predict', 0.5, 0.6, 1.0) | ('predict', 0.5, 0.7, 0.3) | ('predict', 0.5, 0.7, 0.4) | ('predict', 0.5, 0.7, 0.5) | ('predict', 0.5, 0.7, 0.6) | ('predict', 0.5, 0.7, 0.7) | ('predict', 0.5, 0.7, 0.8) | ('predict', 0.5, 0.7, 0.9) | ('predict', 0.5, 0.7, 1.0) | ('predict', 0.5, 0.8, 0.3) | ('predict', 0.5, 0.8, 0.4) | ('predict', 0.5, 0.8, 0.5) | ('predict', 0.5, 0.8, 0.6) | ('predict', 0.5, 0.8, 0.7) | ('predict', 0.5, 0.8, 0.8) | ('predict', 0.5, 0.8, 0.9) | ('predict', 0.5, 0.8, 1.0) | ('predict', 0.5, 0.9, 0.3) | ('predict', 0.5, 0.9, 0.4) | ('predict', 0.5, 0.9, 0.5) | ('predict', 0.5, 0.9, 0.6) | ('predict', 0.5, 0.9, 0.7) | ('predict', 0.5, 0.9, 0.8) | ('predict', 0.5, 0.9, 0.9) | ('predict', 0.5, 0.9, 1.0) | ('predict', 0.5, 1.0, 0.3) | ('predict', 0.5, 1.0, 0.4) | ('predict', 0.5, 1.0, 0.5) | ('predict', 0.5, 1.0, 0.6) | ('predict', 0.5, 1.0, 0.7) | ('predict', 0.5, 1.0, 0.8) | ('predict', 0.5, 1.0, 0.9) | ('predict', 0.5, 1.0, 1.0) | ('predict', 0.6, 0.3, 0.3) | ('predict', 0.6, 0.3, 0.4) | ('predict', 0.6, 0.3, 0.5) | ('predict', 0.6, 0.3, 0.6) | ('predict', 0.6, 0.3, 0.7) | ('predict', 0.6, 0.3, 0.8) | ('predict', 0.6, 0.3, 0.9) | ('predict', 0.6, 0.3, 1.0) | ('predict', 0.6, 0.4, 0.3) | ('predict', 0.6, 0.4, 0.4) | ('predict', 0.6, 0.4, 0.5) | ('predict', 0.6, 0.4, 0.6) | ('predict', 0.6, 0.4, 0.7) | ('predict', 0.6, 0.4, 0.8) | ('predict', 0.6, 0.4, 0.9) | ('predict', 0.6, 0.4, 1.0) | ('predict', 0.6, 0.5, 0.3) | ('predict', 0.6, 0.5, 0.4) | ('predict', 0.6, 0.5, 0.5) | ('predict', 0.6, 0.5, 0.6) | ('predict', 0.6, 0.5, 0.7) | ('predict', 0.6, 0.5, 0.8) | ('predict', 0.6, 0.5, 0.9) | ('predict', 0.6, 0.5, 1.0) | ('predict', 0.6, 0.6, 0.3) | ('predict', 0.6, 0.6, 0.4) | ('predict', 0.6, 0.6, 0.5) | ('predict', 0.6, 0.6, 0.6) | ('predict', 0.6, 0.6, 0.7) | ('predict', 0.6, 0.6, 0.8) | ('predict', 0.6, 0.6, 0.9) | ('predict', 0.6, 0.6, 1.0) | ('predict', 0.6, 0.7, 0.3) | ('predict', 0.6, 0.7, 0.4) | ('predict', 0.6, 0.7, 0.5) | ('predict', 0.6, 0.7, 0.6) | ('predict', 0.6, 0.7, 0.7) | ('predict', 0.6, 0.7, 0.8) | ('predict', 0.6, 0.7, 0.9) | ('predict', 0.6, 0.7, 1.0) | ('predict', 0.6, 0.8, 0.3) | ('predict', 0.6, 0.8, 0.4) | ('predict', 0.6, 0.8, 0.5) | ('predict', 0.6, 0.8, 0.6) | ('predict', 0.6, 0.8, 0.7) | ('predict', 0.6, 0.8, 0.8) | ('predict', 0.6, 0.8, 0.9) | ('predict', 0.6, 0.8, 1.0) | ('predict', 0.6, 0.9, 0.3) | ('predict', 0.6, 0.9, 0.4) | ('predict', 0.6, 0.9, 0.5) | ('predict', 0.6, 0.9, 0.6) | ('predict', 0.6, 0.9, 0.7) | ('predict', 0.6, 0.9, 0.8) | ('predict', 0.6, 0.9, 0.9) | ('predict', 0.6, 0.9, 1.0) | ('predict', 0.6, 1.0, 0.3) | ('predict', 0.6, 1.0, 0.4) | ('predict', 0.6, 1.0, 0.5) | ('predict', 0.6, 1.0, 0.6) | ('predict', 0.6, 1.0, 0.7) | ('predict', 0.6, 1.0, 0.8) | ('predict', 0.6, 1.0, 0.9) | ('predict', 0.6, 1.0, 1.0) | ('predict', 0.7, 0.3, 0.3) | ('predict', 0.7, 0.3, 0.4) | ('predict', 0.7, 0.3, 0.5) | ('predict', 0.7, 0.3, 0.6) | ('predict', 0.7, 0.3, 0.7) | ('predict', 0.7, 0.3, 0.8) | ('predict', 0.7, 0.3, 0.9) | ('predict', 0.7, 0.3, 1.0) | ('predict', 0.7, 0.4, 0.3) | ('predict', 0.7, 0.4, 0.4) | ('predict', 0.7, 0.4, 0.5) | ('predict', 0.7, 0.4, 0.6) | ('predict', 0.7, 0.4, 0.7) | ('predict', 0.7, 0.4, 0.8) | ('predict', 0.7, 0.4, 0.9) | ('predict', 0.7, 0.4, 1.0) | ('predict', 0.7, 0.5, 0.3) | ('predict', 0.7, 0.5, 0.4) | ('predict', 0.7, 0.5, 0.5) | ('predict', 0.7, 0.5, 0.6) | ('predict', 0.7, 0.5, 0.7) | ('predict', 0.7, 0.5, 0.8) | ('predict', 0.7, 0.5, 0.9) | ('predict', 0.7, 0.5, 1.0) | ('predict', 0.7, 0.6, 0.3) | ('predict', 0.7, 0.6, 0.4) | ('predict', 0.7, 0.6, 0.5) | ('predict', 0.7, 0.6, 0.6) | ('predict', 0.7, 0.6, 0.7) | ('predict', 0.7, 0.6, 0.8) | ('predict', 0.7, 0.6, 0.9) | ('predict', 0.7, 0.6, 1.0) | ('predict', 0.7, 0.7, 0.3) | ('predict', 0.7, 0.7, 0.4) | ('predict', 0.7, 0.7, 0.5) | ('predict', 0.7, 0.7, 0.6) | ('predict', 0.7, 0.7, 0.7) | ('predict', 0.7, 0.7, 0.8) | ('predict', 0.7, 0.7, 0.9) | ('predict', 0.7, 0.7, 1.0) | ('predict', 0.7, 0.8, 0.3) | ('predict', 0.7, 0.8, 0.4) | ('predict', 0.7, 0.8, 0.5) | ('predict', 0.7, 0.8, 0.6) | ('predict', 0.7, 0.8, 0.7) | ('predict', 0.7, 0.8, 0.8) | ('predict', 0.7, 0.8, 0.9) | ('predict', 0.7, 0.8, 1.0) | ('predict', 0.7, 0.9, 0.3) | ('predict', 0.7, 0.9, 0.4) | ('predict', 0.7, 0.9, 0.5) | ('predict', 0.7, 0.9, 0.6) | ('predict', 0.7, 0.9, 0.7) | ('predict', 0.7, 0.9, 0.8) | ('predict', 0.7, 0.9, 0.9) | ('predict', 0.7, 0.9, 1.0) | ('predict', 0.7, 1.0, 0.3) | ('predict', 0.7, 1.0, 0.4) | ('predict', 0.7, 1.0, 0.5) | ('predict', 0.7, 1.0, 0.6) | ('predict', 0.7, 1.0, 0.7) | ('predict', 0.7, 1.0, 0.8) | ('predict', 0.7, 1.0, 0.9) | ('predict', 0.7, 1.0, 1.0) | ('predict', 0.8, 0.3, 0.3) | ('predict', 0.8, 0.3, 0.4) | ('predict', 0.8, 0.3, 0.5) | ('predict', 0.8, 0.3, 0.6) | ('predict', 0.8, 0.3, 0.7) | ('predict', 0.8, 0.3, 0.8) | ('predict', 0.8, 0.3, 0.9) | ('predict', 0.8, 0.3, 1.0) | ('predict', 0.8, 0.4, 0.3) | ('predict', 0.8, 0.4, 0.4) | ('predict', 0.8, 0.4, 0.5) | ('predict', 0.8, 0.4, 0.6) | ('predict', 0.8, 0.4, 0.7) | ('predict', 0.8, 0.4, 0.8) | ('predict', 0.8, 0.4, 0.9) | ('predict', 0.8, 0.4, 1.0) | ('predict', 0.8, 0.5, 0.3) | ('predict', 0.8, 0.5, 0.4) | ('predict', 0.8, 0.5, 0.5) | ('predict', 0.8, 0.5, 0.6) | ('predict', 0.8, 0.5, 0.7) | ('predict', 0.8, 0.5, 0.8) | ('predict', 0.8, 0.5, 0.9) | ('predict', 0.8, 0.5, 1.0) | ('predict', 0.8, 0.6, 0.3) | ('predict', 0.8, 0.6, 0.4) | ('predict', 0.8, 0.6, 0.5) | ('predict', 0.8, 0.6, 0.6) | ('predict', 0.8, 0.6, 0.7) | ('predict', 0.8, 0.6, 0.8) | ('predict', 0.8, 0.6, 0.9) | ('predict', 0.8, 0.6, 1.0) | ('predict', 0.8, 0.7, 0.3) | ('predict', 0.8, 0.7, 0.4) | ('predict', 0.8, 0.7, 0.5) | ('predict', 0.8, 0.7, 0.6) | ('predict', 0.8, 0.7, 0.7) | ('predict', 0.8, 0.7, 0.8) | ('predict', 0.8, 0.7, 0.9) | ('predict', 0.8, 0.7, 1.0) | ('predict', 0.8, 0.8, 0.3) | ('predict', 0.8, 0.8, 0.4) | ('predict', 0.8, 0.8, 0.5) | ('predict', 0.8, 0.8, 0.6) | ('predict', 0.8, 0.8, 0.7) | ('predict', 0.8, 0.8, 0.8) | ('predict', 0.8, 0.8, 0.9) | ('predict', 0.8, 0.8, 1.0) | ('predict', 0.8, 0.9, 0.3) | ('predict', 0.8, 0.9, 0.4) | ('predict', 0.8, 0.9, 0.5) | ('predict', 0.8, 0.9, 0.6) | ('predict', 0.8, 0.9, 0.7) | ('predict', 0.8, 0.9, 0.8) | ('predict', 0.8, 0.9, 0.9) | ('predict', 0.8, 0.9, 1.0) | ('predict', 0.8, 1.0, 0.3) | ('predict', 0.8, 1.0, 0.4) | ('predict', 0.8, 1.0, 0.5) | ('predict', 0.8, 1.0, 0.6) | ('predict', 0.8, 1.0, 0.7) | ('predict', 0.8, 1.0, 0.8) | ('predict', 0.8, 1.0, 0.9) | ('predict', 0.8, 1.0, 1.0) | ('predict', 0.9, 0.3, 0.3) | ('predict', 0.9, 0.3, 0.4) | ('predict', 0.9, 0.3, 0.5) | ('predict', 0.9, 0.3, 0.6) | ('predict', 0.9, 0.3, 0.7) | ('predict', 0.9, 0.3, 0.8) | ('predict', 0.9, 0.3, 0.9) | ('predict', 0.9, 0.3, 1.0) | ('predict', 0.9, 0.4, 0.3) | ('predict', 0.9, 0.4, 0.4) | ('predict', 0.9, 0.4, 0.5) | ('predict', 0.9, 0.4, 0.6) | ('predict', 0.9, 0.4, 0.7) | ('predict', 0.9, 0.4, 0.8) | ('predict', 0.9, 0.4, 0.9) | ('predict', 0.9, 0.4, 1.0) | ('predict', 0.9, 0.5, 0.3) | ('predict', 0.9, 0.5, 0.4) | ('predict', 0.9, 0.5, 0.5) | ('predict', 0.9, 0.5, 0.6) | ('predict', 0.9, 0.5, 0.7) | ('predict', 0.9, 0.5, 0.8) | ('predict', 0.9, 0.5, 0.9) | ('predict', 0.9, 0.5, 1.0) | ('predict', 0.9, 0.6, 0.3) | ('predict', 0.9, 0.6, 0.4) | ('predict', 0.9, 0.6, 0.5) | ('predict', 0.9, 0.6, 0.6) | ('predict', 0.9, 0.6, 0.7) 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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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| 1991-01-31 00:00:00 | 1902 | 1577.000000 | 1446.452122 | 1406.612961 | 1399.934204 | 1410.675751 | 1454.142587 | 1512.260366 | 1455.847280 | 1806.735854 | 1433.531119 | 1381.619054 | 1370.336619 | 1391.936253 | 1083.053373 | 684.320336 | -190.960167 | -3879.780847 | 1459.480300 | 1405.329736 | 1398.056852 | 1414.492540 | 1180.369557 | 613.283318 | -480.366339 | 4330.084000 | 1529.235387 | 1458.765311 | 1504.540450 | 1924.521326 | 2136.823681 | 1907.168337 | 852.190788 | 413.205042 | 1127.544854 | 862.991786 | 1024.231016 | 2130.220874 | 3720.428743 | 4459.523666 | 4416.742906 | 2434.847002 | 1147.363881 | 378.990232 | -2356.866728 | 1620.446942 | 15632.367092 | 1381.536517 | 34408.325139 | 8016.213750 | 1398.805970 | 395.957262 | -164.598196 | 237.937342 | -6239.589122 | 3051.446733 | 19320.354551 | -512.158422 | 1766.532704 | 1003.725094 | 2086.712986 | -3457.178655 | -3330.313288 | -1886.576098 | 7457.056389 | 1682.164224 | 1516.786995 | 1451.146275 | 1415.504592 | 1394.809984 | 1371.909668 | 1197.293469 | 916.192758 | 478.280221 | 1550.701092 | 1481.774743 | 1437.953930 | 1405.774840 | 1492.051598 | 1022.304639 | 1333.879375 | 946.816287 | 1586.195833 | 1184.940878 | 1034.199181 | 1042.316265 | 1338.330049 | 1850.830120 | 2155.864626 | 1983.811000 | 1502.027021 | 1164.959429 | 704.967262 | -26.985941 | -1364.776278 | -3089.646937 | 776.699153 | 3424.303439 | 1682.343740 | 1356.649281 | 776.257416 | -581.817200 | -5686.280206 | -10163.193845 | 65004.979686 | 8597.499161 | 1853.226865 | 1649.369132 | 1210.675502 | 551.633149 | -7584.362077 | 709.414088 | -5663.646947 | -5903.670251 | 1942.466630 | 1877.079273 | 1646.636960 | -166.117262 | -1637.638730 | 4330.727395 | 106.338318 | -1552.510725 | 1949.466096 | 1992.798735 | 1973.446101 | 209.418806 | -622.284719 | -4896.625219 | -5674.660007 | -1005.337233 | 1575.706816 | 1518.416790 | 1477.310171 | 1415.254349 | 1331.007665 | 1176.714657 | 1117.747583 | 857.623901 | 1599.892887 | 1540.783298 | 1215.617396 | 1069.881940 | 953.348552 | 892.754966 | 882.499222 | 813.400251 | 1617.086205 | 1562.107962 | 1212.412423 | 886.313322 | 432.491116 | -83.301128 | -276.308933 | 3567.273927 | 1640.541919 | 1619.716696 | 1417.030933 | 1112.703743 | 610.959710 | -280.878646 | -305.861805 | -133.158800 | 1664.706714 | 1778.783089 | 1702.518395 | 1619.342484 | 462.439508 | 768.822640 | 397.644119 | 346.093594 | 1703.677792 | 1866.001453 | 1936.212326 | 2267.317643 | 3446.775985 | 1940.958555 | 1712.306084 | 1024.310995 | 1738.061798 | 1871.768574 | 2056.216102 | -7786.439723 | 14005.723969 | -1076.596664 | 3019.274379 | 2247.205739 | 1831.676504 | 1712.556702 | 1926.379626 | -421.193698 | -26780.349546 | -5400.794371 | 2163.284189 | 7308.564369 | 1600.313992 | 1555.671454 | 1514.913961 | 1465.026173 | 1348.156118 | 1231.725128 | 1073.954569 | 850.423775 | 1626.417668 | 1578.838602 | 1415.029827 | 1277.938536 | 1148.172573 | 1032.759339 | 943.925292 | 801.925577 | 1661.590055 | 1611.625908 | 1550.741674 | 1450.168197 | 1411.262403 | 1462.765626 | 1563.964591 | 1160.026043 | 1683.525707 | 1651.636664 | 1624.241492 | 1697.252769 | 1959.302579 | 2266.967112 | 10910.883536 | 2197.528177 | 1719.637683 | 1686.510608 | 1636.260574 | 1757.805429 | 2525.814178 | 105023.077883 | -3767.316026 | 6865.051794 | 1745.839528 | 1696.771751 | 1645.548964 | 1303.286614 | 737.480416 | 2101.863049 | 1397.788792 | -2003.493648 | 1845.076301 | 1910.619228 | 1506.206680 | 80.179542 | 54.320282 | 1912.036133 | -1417.695887 | 982.229491 | 1881.522408 | 2136.479494 | 1590.060808 | -275.559172 | -1739.414934 | 22528.515419 | 17.943434 | 2374.815757 | 1618.829200 | 1582.216156 | 1561.933627 | 1532.316449 | 1466.760400 | 1378.330912 | 1585.030822 | 1543.207790 | 1641.903935 | 1613.724880 | 1594.392363 | 1569.954999 | 1497.641049 | 1599.577160 | 2200.926411 | 2576.020117 | 1679.053908 | 1653.674419 | 1634.660413 | 1598.896552 | 1530.267959 | 1798.302722 | 33621.579029 | 49899.082001 | 1712.494482 | 1692.281417 | 1659.765059 | 1545.738698 | 1133.429743 | 1626.457874 | 481.504137 | -266.398723 | 1735.397694 | 1925.853858 | 1904.742217 | 1435.734141 | -272.859530 | 1821.116795 | 708.968107 | 1133.830117 | 1761.660456 | 2091.411393 | 2214.519070 | 1514.920900 | 1211.354399 | -22068.686551 | 639.593139 | 2501.551637 | 1717.092755 | 2363.324736 | 2917.598354 | 2024.064754 | 1255.389708 | -1436.541531 | -417.453440 | 4088.287709 | 1631.113128 | 3032.099483 | -1680.910428 | 4549.776037 | -14659.758497 | -2901.883680 | 444.291043 | 12286.767856 | 1623.097713 | 1600.578527 | 1598.573598 | 1617.493718 | 1614.021720 | 1539.815251 | 1818.514842 | 3321.121082 | 1653.217464 | 1640.169563 | 1652.621212 | 1637.309505 | 1498.770932 | 1189.076099 | -874.334905 | 626.466936 | 1684.389137 | 1681.890743 | 1890.963893 | 1799.632156 | 1353.008717 | -1644.303577 | -5672.114867 | 3372.232016 | 1712.266767 | 1890.282278 | 2139.857397 | 2044.188648 | 1039.749735 | -6070.794553 | -3472.907638 | 9506.445948 | 1635.291149 | 2012.402123 | 2271.094851 | -5730.242440 | 1344.352826 | 3040.575872 | -118.905432 | -14703.310259 | 1532.278899 | 2244.309713 | 4036.222196 | 3238.791759 | -1219.644481 | 281.014699 | 18580.678441 | -3880.301254 | 1792.391814 | 4409.897266 | 575.122266 | 5048.407656 | 114.570123 | 4613.373994 | -59818.766444 | -2089.117485 | 1107.354516 | -7741.631904 | 268.837770 | 1180.408113 | -4850.481309 | 63918.509178 | -14594.266472 | -1131.213620 | 1611.771613 | 1602.696362 | 1636.826292 | 1797.838997 | 1798.771015 | 1542.397222 | 4269.513042 | -2300.248181 | 1638.002414 | 1640.946959 | 1684.704600 | 2025.311128 | 1942.080260 | 661.860172 | -8617.539419 | -3731.054899 | 1661.310621 | 1734.280873 | 2105.422083 | 2490.197930 | 2632.477044 | -3350.844019 | -24639.097330 | -2680.725644 | 1673.254732 | 1680.421048 | 2575.889508 | 215296.876778 | -1225.496395 | 21805.498431 | 259635.830014 | -1710.039732 | 1388.621629 | 1770.488030 | 2845.292700 | 9864.588234 | -2425.993003 | 1258.103450 | 6831.273098 | -1064.606593 | 1172.028634 | 2272.503844 | -1549.025789 | 6467.650663 | 2529.551228 | 9658.920398 | -1005.238749 | -650.095107 | 833.272044 | 57266.637592 | 790.048145 | -1631.301088 | 3422.447083 | 710.144585 | 132.439308 | -498.404605 | 292.442698 | -304.300890 | 26.821339 | 2995.314023 | 16137.916741 | 5768.701180 | 4186.797733 | -757.223376 | 1579.904420 | 1579.224749 | 1626.044860 | 2007.410983 | 2532.998882 | 2862.666126 | -2790.186177 | -1043.557704 | 1601.455491 | 1605.896805 | 1797.609342 | 2526.686728 | 4110.018369 | 5381.068230 | 15816.665314 | -1029.122092 | 1613.593046 | 1444.673450 | 2039.323763 | 1944.203369 | 5377.525884 | -5417.836403 | 427.228183 | -888.101464 | 1614.126047 | 1290.727488 | 3290.905870 | 927.063054 | 1309.260152 | -216.283615 | 12.182600 | -855.133478 | 1084.766208 | 1155.547006 | 33872.817716 | -2090.493020 | -202.485744 | 3104.978687 | 186.086620 | -1038.791523 | 821.529834 | 1290.669076 | 35946.554918 | 2030.675609 | 1729.472622 | -10949.143488 | -32455.757077 | -1400.304721 | 459.188811 | -20445.260941 | 5453.613920 | -1028.844371 | -1124.235635 | -15180.355008 | -19323.684046 | -1758.411951 | -4731.659223 | 80661.809663 | 111854.873192 | 1211.542283 | 1205.518077 | 4664.385018 | -19.084854 | -2008.043976 |
| 1991-02-28 00:00:00 | 2049 | 1334.000000 | 1259.797124 | 1165.136416 | 1107.138846 | 1070.580743 | 1078.178470 | 1114.130786 | 858.002585 | 982.611598 | 1259.262051 | 1145.279371 | 1079.341402 | 1048.977926 | 721.484630 | 305.766223 | -367.117145 | -1602.033130 | 1308.387516 | 1187.488251 | 1120.743861 | 1084.655702 | 985.909943 | 492.397410 | -257.557135 | 17312.375981 | 1407.008881 | 1263.229346 | 1150.758132 | 1724.640672 | 2244.080434 | 2173.699365 | 949.948056 | 554.046520 | 991.551992 | 541.614620 | 415.412299 | 1465.100131 | 5007.731673 | 8327.887399 | 2551.332302 | 2851.604855 | 1120.299022 | 230.205840 | -1355.227542 | 6234.997760 | -1666.166153 | 1790.960790 | -2298.233983 | -17194.429662 | 1515.709056 | 437.070334 | -157.109809 | -9794.992317 | 516.785499 | -35706.990135 | -1420.295740 | 376.877894 | 2013.966047 | 1183.681909 | 1422.492071 | 4709.800543 | -580.180357 | 379.232128 | 7349.198520 | 2134.049264 | 1363.588725 | 1240.061966 | 1146.647820 | 1079.643767 | 1017.456188 | 870.951208 | 602.390567 | 241.386456 | 1420.315015 | 1288.008191 | 1178.088739 | 1090.889346 | 1164.573306 | 622.787757 | 1103.778008 | 726.515939 | 1472.435215 | 966.478453 | 699.412750 | 589.411166 | 791.539722 | 1416.457183 | 1964.403415 | 1711.981625 | 1489.648321 | 1028.708067 | 479.752757 | -201.909798 | -1159.968643 | -2365.430247 | -1467.638425 | 1782.700815 | 1763.419105 | 1340.281461 | 695.529540 | -345.815788 | -2466.461560 | -3709.759782 | -18948.056333 | -3892.619037 | 1996.408500 | 1748.480076 | 1251.874435 | 489.566370 | -4416.081495 | 972.040074 | -2064.581670 | -1626.394924 | 2094.336801 | 2047.031669 | 1817.291246 | 735.124528 | -987.497490 | -14190.128266 | 91.394096 | -830.749381 | 2067.862800 | 2175.999301 | 2273.065198 | 1737.143181 | -780.929165 | -4170.827539 | -7305.913496 | -663.195788 | 1445.609046 | 1327.076385 | 1227.293750 | 1118.705882 | 1016.067867 | 864.472651 | 875.544988 | 645.402523 | 1490.891914 | 1363.666584 | 948.069573 | 742.306888 | 598.974309 | 547.039679 | 602.313154 | 598.322473 | 1523.772679 | 1401.140307 | 1019.860338 | 656.853358 | 245.042620 | -197.170140 | -393.954147 | 9989.041379 | 1572.984591 | 1610.954316 | 1326.999593 | 1002.878821 | 610.984637 | 62.132840 | -212.184139 | -69.116385 | 1623.960311 | 1832.232415 | 1702.260723 | 1633.743163 | -311.400756 | 1470.269479 | 1554.152832 | 587.607255 | 1702.132184 | 1928.193399 | 1962.615495 | 2406.789804 | 5000.346970 | 3126.773149 | 1707.999941 | 2042.197520 | 1772.424696 | 1892.349610 | 1976.402879 | -7868.464007 | -9225.195664 | -142091.976137 | -4436.411709 | 11872.584173 | 1856.848145 | 1713.797651 | 1529.954505 | -220.840030 | 27252.641881 | 11104.350144 | 2060.899531 | -5558.631342 | 1483.015353 | 1372.919607 | 1268.790878 | 1187.194345 | 1070.248701 | 1009.468628 | 973.180077 | 874.509236 | 1541.442824 | 1415.293090 | 1208.414194 | 1012.807689 | 885.517569 | 857.861527 | 974.644497 | 1043.983310 | 1608.275382 | 1478.373705 | 1416.748100 | 1247.847674 | 1221.227525 | 1481.217415 | 2212.139645 | 2242.563558 | 1666.091974 | 1561.496852 | 1486.264299 | 1514.571172 | 1770.805289 | 2699.723143 | -273541.367342 | 11716.016524 | 1748.255417 | 1643.014622 | 1524.854009 | 1480.304112 | 1981.974612 | -1522.306807 | 1887.066558 | -4917.623247 | 1818.587447 | 1684.884162 | 1602.116853 | 891.123335 | -2175.815868 | -5169.866347 | 1730.919146 | -789.996018 | 1822.309435 | 2078.788178 | 1682.109795 | -37.753371 | -4814.371284 | -986.589279 | 6451.232129 | 2215.516600 | 1785.347736 | 2551.158995 | 2466.424733 | -788.202947 | 1393.224039 | 28255.828706 | 2030.065455 | 15893.969940 | 1528.702767 | 1406.710506 | 1315.749512 | 1253.944500 | 1198.687935 | 1065.377840 | 1804.460233 | 2944.155570 | 1581.084452 | 1469.232375 | 1379.739355 | 1331.848716 | 1249.737171 | 1402.610357 | 3222.634946 | 19592.069592 | 1667.176191 | 1556.236316 | 1467.131326 | 1384.542360 | 1296.617179 | 1286.816591 | -36245.213659 | -3961.834461 | 1753.707826 | 1652.189942 | 1523.193757 | 1434.672683 | 773.080773 | -602.598000 | -23422.634560 | 132.503574 | 1824.184202 | 1950.594045 | 2092.630026 | 1568.045960 | -132.107142 | -1436.123318 | -6219.106705 | 3333.332198 | 1594.887912 | 2135.104233 | 2845.781391 | 2375.794853 | 3419.851869 | -48204.504292 | -2874.989323 | -5882.856866 | 1350.360997 | 2357.746705 | 4644.929420 | 4731.965545 | -6156.533926 | 1952.683679 | 46.679593 | -2497.982150 | 917.145625 | 4569.391735 | 4158.940303 | 26568.394085 | -19237.880841 | -5036.175893 | 275.619630 | -1843.621053 | 1558.553969 | 1433.418918 | 1337.954209 | 1313.991050 | 1334.603200 | 1250.547865 | 1675.770817 | 7533.232831 | 1636.499917 | 1517.599083 | 1446.245132 | 1418.250342 | 1251.823880 | 774.179369 | -429.359052 | -4988.145109 | 1720.179215 | 1615.889512 | 1834.570417 | 1798.593150 | 1251.666846 | -832.419915 | 15965.180850 | -5449.252688 | 1809.431035 | 1764.098607 | 2249.569054 | 2491.240618 | 1299.345146 | -4325.739546 | -2184.331569 | -3797.610786 | 1409.843229 | 1752.549118 | 2528.134111 | -81569.944703 | 1831.103241 | 3012.208415 | 6850.222221 | -3022.792425 | 1115.941422 | 1691.697435 | 6671.052636 | 4983.142384 | -3411.148360 | -3886.285431 | 36471.453295 | -2882.400083 | 2260.154607 | -546.212674 | -146.646560 | 76508.412348 | -2511.343944 | 1164.722659 | -96245.398956 | -3435.800261 | 87.604352 | 1811.063006 | 627.827781 | 45087.324417 | -618520.407014 | -14302.983208 | 58830.159452 | -7107.343340 | 1583.125719 | 1451.970114 | 1369.607950 | 1503.477634 | 1537.073918 | 1290.996247 | 11943.949276 | -3196.946208 | 1671.253203 | 1548.885874 | 1464.119025 | 1903.522335 | 1967.982226 | 618.627049 | -5862.984768 | -4861.599081 | 1757.850885 | 1505.852110 | 1941.359325 | 2833.299343 | 3812.561582 | -3344.021801 | -20150.114311 | -5639.236940 | 1831.469591 | 1695.018889 | 2545.436995 | 83602.773749 | -5864.644531 | 26273.228011 | 200952.648648 | -10167.127466 | 1098.462522 | 1087.518841 | 2422.161134 | -3020.120268 | 41.144729 | 2084.232138 | -3537.553063 | 7642.955969 | 751.846181 | 1207.794765 | -845.090430 | -4406.468821 | -2578.616811 | -76901.185519 | 10317.486697 | 1374.075117 | 286.324102 | 12895.522920 | -1862.989366 | -6597.124380 | -6360.422738 | 1807.834232 | 355.580908 | 637.814459 | -386.493570 | -3736.118609 | -1812.955733 | 3766.179466 | 45725.219460 | -11073.711002 | -7000.185296 | 804.063421 | 1607.321258 | 1470.410436 | 1367.950038 | 1542.862794 | 2127.008439 | 3355.424129 | -13634.296195 | 3884.426302 | 1710.382515 | 1571.551383 | 1404.632193 | 2197.421702 | 4658.570898 | 9879.712351 | -4844.712617 | 2496.429789 | 1801.228904 | 1121.237618 | 1637.228640 | 1666.683529 | 38517.399176 | 2322.591220 | 248.329035 | 1488.893371 | 1873.943593 | 866.485761 | 3892.476921 | -395.070124 | -6086.100688 | -25.014072 | -170.615977 | 1078.933222 | 908.183162 | 712.687947 | -7545.055366 | -111022.533915 | -4087.683194 | -4697.926970 | 4162.985757 | 1105.234282 | 601.185218 | 1090.199206 | 16160.427687 | -493.980999 | 90.930505 | 547.656408 | -24788.957913 | 1395.617141 | 185.685810 | -37025.288285 | -75506.835225 | -65785.668134 | 34075.519237 | 90380.229048 | -1858.878544 | 1760.494396 | -13018.530629 | -230881.309051 | -22091.531885 | -137.282931 | -9007.163811 | -9620.836528 | -189.274747 | 2047.979514 |
| 1991-03-31 00:00:00 | 1874 | 1746.000000 | 1656.945348 | 1555.360103 | 1491.763706 | 1443.605265 | 1456.672400 | 1515.177196 | 916.047330 | 921.118269 | 1672.295075 | 1532.845068 | 1451.556354 | 1406.025684 | 900.705935 | 228.640040 | -682.377563 | -1822.562789 | 1768.166925 | 1617.171388 | 1533.076248 | 1480.570307 | 1550.232886 | 790.382327 | -312.893791 | -11590.473893 | 1943.749900 | 1760.673783 | 1486.779511 | 2735.034384 | 4411.876589 | 4899.358204 | 2177.797594 | 1138.082831 | 1365.739608 | 564.613804 | 114.444591 | 1296.215717 | 101502.048122 | 147905.331362 | 60606.935739 | 7337.087173 | 1689.350685 | 252.535699 | -1772.541906 | -11719.085984 | 850.634441 | 4982.108327 | -1695.734203 | -6353.932991 | 2470.487133 | 755.694471 | -274.471098 | -928.874498 | 1507363.699604 | 849.132578 | 112788.924339 | 1365.336700 | 3430.201874 | 2152.433620 | 2186.876936 | 5497.149225 | -133.386681 | 4738.223842 | -44441.523665 | 6851.249725 | 1855.326993 | 1721.947920 | 1605.080514 | 1510.816871 | 1406.390251 | 1241.932811 | 815.579547 | 257.616985 | 1970.574662 | 1822.361107 | 1672.069419 | 1534.883408 | 1697.168871 | 742.206383 | 1904.830912 | 1199.131459 | 2076.384788 | 1333.874048 | 848.314752 | 574.122385 | 787.353895 | 2048.407788 | 3871.226705 | 3308.375417 | 2281.220883 | 1540.631555 | 617.862172 | -451.463300 | -1777.403762 | -3477.620092 | -3911.624899 | 2007.430679 | 2841.402628 | 2204.933646 | 1134.167720 | -452.638138 | -3125.723437 | -6282.636785 | -17872.532038 | -4429.459257 | 3326.024033 | 3067.472434 | 2273.865160 | 849.035418 | -6365.552040 | 2081.236792 | -2857.030266 | -2329.235768 | 3546.835167 | 3745.167977 | 3536.562302 | 2470.270485 | -1370.678397 | -12965.094828 | 207.408401 | -1525.502852 | 3508.714678 | 4086.889836 | 4724.503798 | 5888.845510 | -1973.397849 | -11912.157752 | 1241.622451 | -1555.310724 | 2025.528180 | 1911.205401 | 1788.632236 | 1617.631618 | 1455.844940 | 1230.738099 | 1424.876008 | 1115.608937 | 2135.790373 | 2002.957710 | 1344.834225 | 966.710925 | 697.250470 | 617.890311 | 864.720078 | 1127.871380 | 2226.513851 | 2103.509636 | 1573.582660 | 940.492448 | 268.056759 | -455.572906 | -950.285850 | -7836.220927 | 2362.231682 | 2714.766951 | 2258.898400 | 1697.577635 | 1096.878108 | 447.522344 | -338.692031 | -101.691272 | 2508.234087 | 3228.109688 | 3095.480419 | 3026.181067 | -1462.002395 | 3734.486479 | 5589.855040 | 3227.761954 | 2726.476921 | 3469.746558 | 3661.431565 | 4582.545444 | 11309.032192 | 9470.491779 | -13793.052573 | -47491.319365 | 2938.077085 | 3394.521861 | 3531.737544 | -5166.940029 | 1066844.974349 | 598.343117 | -2677.597274 | -8218.046020 | 3079.924448 | 3070.063369 | 2303.188502 | 918.031112 | 23368.770874 | -2957.478932 | -3407.820805 | -5622.273175 | 2131.029025 | 2040.220587 | 1902.017415 | 1768.509345 | 1565.104066 | 1524.799356 | 1657.524045 | 2113.873132 | 2291.725274 | 2160.754422 | 1902.248782 | 1515.217369 | 1238.745295 | 1208.304260 | 1782.672889 | 3748.947409 | 2469.865005 | 2340.484723 | 2398.415456 | 2026.104085 | 1847.892272 | 2225.852306 | 4505.947118 | 21596.922611 | 2655.310851 | 2588.218904 | 2530.476881 | 2553.618953 | 2561.499496 | 2907.446465 | 11534.329464 | -16688.836578 | 2909.619559 | 2861.102018 | 2712.866801 | 2417.104657 | 1943.109607 | 750.456752 | 21166.927768 | -8852.905346 | 3163.771756 | 3064.712376 | 3116.566114 | 1350.529790 | -1130.904957 | -8901.467748 | -3001.498135 | -6599.170672 | 2956.269938 | 4104.243212 | 3923.369992 | -260.655178 | -2815.085180 | -1990.899145 | -30117.363298 | -5845.678186 | 2756.769896 | 5525.826703 | 8318.572464 | -66480.190927 | -6510.224165 | 14189.042997 | 798.573814 | -4442.857577 | 2283.953745 | 2166.899162 | 2037.358830 | 1901.179222 | 1738.898026 | 1140.398631 | 2216.266396 | 5882.561372 | 2446.051816 | 2358.028012 | 2233.893970 | 2128.259718 | 1851.845064 | 1452.686222 | 2100.127736 | 10198.497343 | 2707.242935 | 2635.552130 | 2528.168609 | 2309.486216 | 1941.804907 | 969.232519 | 490.556257 | 6153.903049 | 3004.692814 | 2977.675872 | 2762.916607 | 2718.400983 | 1122.909459 | -595.385049 | -1257.987404 | -488.401408 | 3291.679618 | 3562.162847 | 4479.634325 | 3724.981727 | -217.498428 | -2823.868872 | -2732.244814 | -8577.377710 | 2435.098329 | 3838.401431 | 7113.069307 | 8526.911236 | 41039.063229 | -51539.551406 | -2695.350424 | -2784.095038 | 1795.818651 | 3639.522485 | 15041.775269 | 50381.652278 | -18396.028531 | -366.443590 | -922.904413 | -2618.449440 | 793.159381 | 2209.513077 | 7565.321006 | -3518.256845 | -10016.994802 | -22703.731957 | -2108.651981 | -3498.544948 | 2425.086208 | 2310.784461 | 2147.086429 | 2021.284749 | 1893.490780 | 1283.073255 | 1016.360819 | 1462.800457 | 2684.764591 | 2593.312144 | 2501.734830 | 2404.643236 | 1873.371753 | 816.130208 | -382.352405 | -590.976600 | 2985.106279 | 2964.901011 | 3428.073112 | 3496.438470 | 2355.014319 | -1399.833008 | 5431.183421 | -2338.190551 | 3354.220497 | 3062.389453 | 4422.611304 | 5861.541231 | 3680.909138 | -8540.506497 | -2515.617686 | -3689.079195 | 2156.357020 | 2767.166380 | 5432.457612 | -22758.918520 | 8017.848490 | 9769.778381 | 31887.665179 | -5591.426400 | 1496.989491 | 1856.685273 | 9777.520722 | 19143.256427 | -110283.125181 | -16066.607367 | 5054.705213 | -14446.141281 | 5677.062573 | 452.141224 | 31971.753312 | 128707.018610 | -1187.176193 | 4428.663120 | -278097.069966 | 15779.151518 | -538.909710 | 5300.382673 | -12.518227 | -5217.887419 | -2344.730818 | 17165.810865 | -16202.712177 | 3680.519557 | 2591.689153 | 2491.869976 | 2348.409108 | 2400.653827 | 2188.581600 | 1499.940314 | 2440.558880 | -1403.752262 | 2932.473057 | 2884.694641 | 2743.935841 | 3343.838539 | 3386.098262 | 1043.878800 | -9228.289144 | -3186.790392 | 3314.907520 | 2620.563320 | 3507.910895 | 5474.013133 | 8790.920698 | -8567.297007 | -64952.443926 | -5420.233086 | 3727.908903 | 3694.145588 | 4319.431374 | -175104.192089 | -26332.426215 | 158145.097680 | -381051.732288 | -10094.626367 | 1704.401715 | 1448.237125 | 3759.374972 | -27982.990384 | 2012.093614 | 19167.197729 | 33418.485123 | -26428.798696 | 988.381601 | 1290.047942 | -4835.717097 | -15731.237288 | -4102.776642 | -305.395616 | 4894.564381 | -13423.230449 | -95.180166 | 6693.676653 | -5087.019634 | -32166.712257 | 324688.423727 | 3905.417741 | -1895.325413 | -2736.655546 | -2312.432495 | -22799.722274 | -17632.732018 | -3785.281801 | -112007.147172 | -26540.010992 | 23481.917056 | -2088.919926 | 2813.614014 | 2762.351222 | 2625.449465 | 2511.013216 | 2931.485454 | 3040.397685 | -2319.522556 | -1703.804321 | 3276.648910 | 3263.096944 | 2627.135849 | 3991.175447 | 7296.498920 | 10037.271052 | 20736.215005 | -2215.484366 | 3785.090136 | 2109.646678 | 3431.156866 | 3176.314445 | -38198.177902 | 2040.000241 | -1252.120061 | -2117.894867 | 4327.668266 | 1677.074159 | 11637.345165 | 1272.116286 | 62969.216588 | -35895.615133 | -377.849205 | -1824.944065 | 1706.526562 | 1349.799244 | -26432.097934 | -995.598108 | -49294.445432 | 7146.748382 | -27481.574858 | -1822.413197 | 1138.542476 | 5204.142479 | -1695266.592788 | -882.433892 | 3780.206666 | -315.540374 | 1267.856274 | -2109.845756 | -4208.997463 | 606140.579227 | -4279.739373 | 2988.273776 | 109442.346954 | 101372.974599 | 273.913284 | -2507.425834 | 60078.283309 | -92295.850963 | -3693.150520 | -5210.023228 | 27194.414281 | 77784.451792 | -2496.816141 | -2897.518715 |
| 1991-04-30 00:00:00 | 1279 | 1630.000000 | 1591.203161 | 1446.227541 | 1337.014720 | 1247.340001 | 1229.949125 | 1276.819310 | 603.956804 | 524.962904 | 1628.849142 | 1434.776657 | 1301.649137 | 1206.634999 | 725.882262 | 63.458646 | -727.832495 | -1518.335996 | 1759.433683 | 1541.565600 | 1395.378688 | 1292.517972 | 1609.290895 | 859.677282 | -275.344966 | -5293.713142 | 1975.820477 | 1714.174852 | 1223.592528 | 2699.131823 | 5758.909053 | 8271.588939 | 2573.020336 | 1527.861523 | 1420.273316 | 404.907927 | -204.641520 | 198.321038 | -4554.683478 | -9896.694169 | -18410.745081 | 22285.055745 | 1945.801562 | 207.566389 | -1646.141273 | -4787.653687 | 8682.867946 | -12047.709346 | -399.589711 | -3955.298206 | 3104.016999 | 952.622411 | -325.841387 | -518.377567 | -5981.007850 | -193092.677472 | -11159.947080 | 2566.170188 | 4565.519353 | 2946.057487 | 2627.028897 | 5790.709781 | 814.472881 | -2369.084486 | -8024.733910 | -497275.545288 | 1820.102909 | 1645.504017 | 1476.890471 | 1341.982248 | 1211.079282 | 1134.079760 | 737.904196 | 188.872387 | 1971.008442 | 1770.885987 | 1553.973426 | 1364.401828 | 1528.894278 | 557.385437 | 2252.522470 | 1457.236992 | 2104.450055 | 1306.414539 | 686.102704 | 315.765785 | 399.911572 | 1766.795220 | 5701.250309 | 5610.951920 | 2610.370773 | 1670.295859 | 559.409184 | -528.686135 | -1649.110671 | -3095.302635 | -5000.802575 | 2040.884169 | 3437.689146 | 2653.118055 | 1304.672021 | -422.582218 | -2808.091838 | -6661.339992 | -15104.452215 | -5118.281664 | 4158.030927 | 3963.579740 | 2938.660189 | 1025.042919 | -6553.310607 | 55.299692 | -3082.620175 | -3199.937206 | 4465.368420 | 5048.107354 | 4943.270282 | 4316.147527 | -1358.572463 | -30750.151017 | 387.253389 | -3279.401052 | 4335.081792 | 5584.364089 | 7022.904452 | 11571.324609 | -3111.638936 | -15854.315148 | -15947.536333 | -17706.817252 | 2001.194659 | 1849.946303 | 1677.006907 | 1456.330356 | 1274.869427 | 1075.102666 | 1498.819541 | 1427.974500 | 2153.343910 | 1971.371362 | 1271.545588 | 803.135732 | 483.541481 | 380.842010 | 766.133002 | 1845.967216 | 2284.672437 | 2112.780545 | 1648.676905 | 885.947601 | 179.544946 | -524.557455 | -1265.812185 | -3124.882520 | 2494.490055 | 3217.904468 | 2628.999447 | 1886.501151 | 1196.055366 | 699.663648 | -343.302368 | -156.590375 | 2731.078640 | 3975.955643 | 3853.970663 | 3668.329363 | -2326.346368 | 4902.259360 | 12332.394730 | -8354.012829 | 3103.440570 | 4304.496379 | 4662.255030 | 5591.696846 | 12521.922186 | 6492.196023 | 26974.207474 | -6193.310103 | 3498.929323 | 4132.861764 | 4343.389977 | 1070.257826 | 4207.032791 | 20457.579031 | -2503.425938 | -7536.572042 | 3353.014888 | 3911.751373 | 2628.090479 | -1243.725832 | 108351.304395 | 56135.464916 | -5008.397546 | -14349.004569 | 2106.940560 | 1992.196088 | 1807.373578 | 1625.337042 | 1389.012556 | 1372.233016 | 1518.889470 | 3083.938382 | 2346.475395 | 2167.965551 | 1977.692317 | 1468.441080 | 1082.241712 | 954.377843 | 1450.260526 | 6651.378830 | 2609.354606 | 2449.611088 | 2704.228069 | 2170.640398 | 1777.869950 | 1816.518944 | 2965.915534 | 31779.916911 | 2932.256843 | 2872.628952 | 2830.607808 | 2933.502972 | 2523.535386 | 1994.030895 | 3008.932139 | 112771.795623 | 3387.624525 | 3399.714350 | 3282.844220 | 2926.440207 | 1882.342842 | 318.513650 | -5830.629256 | 11801.059620 | 3911.293228 | 3899.293398 | 4237.301783 | 1798.717918 | 753.850619 | -12394.830435 | -1563.391498 | 602.634312 | 2986.788413 | 4920.465603 | 6772.629520 | -3017.531572 | 11949.840411 | -2172.312878 | -18789.561601 | -2556.574335 | 2574.100304 | 6539.407537 | 71736.206935 | 7696.227518 | -4017381.323082 | -58991.981908 | -3776.366899 | -3707.667309 | 2296.585140 | 2152.646787 | 1994.572418 | 1820.272452 | 1622.722682 | 849.410118 | 1516.780422 | 3569.564345 | 2548.380347 | 2455.119525 | 2322.175011 | 2218.335877 | 1883.647420 | 1178.560777 | 1285.551123 | 3413.398544 | 2973.147922 | 2930.305170 | 2881.617423 | 2651.742016 | 2141.066267 | 856.496886 | 275.043567 | 1901.861258 | 3517.050043 | 3589.907962 | 3452.235321 | 3678.146195 | 1495.399023 | -951.983759 | -1771.982078 | -383.580917 | 4111.518470 | 3908.184147 | 5995.276917 | 6621.822572 | -437.886346 | -9320.969601 | -5049.812172 | -4021.119217 | 2326.128664 | 3920.671605 | 10349.054357 | 42281.191954 | -23619.548896 | 43768.783860 | 1318.722589 | -4446.662782 | 1535.305008 | 3132.191226 | 19688.318815 | -29932.066082 | 59639.116417 | 3646.967939 | 868.507107 | -12286.482896 | 393.465317 | 1358.824443 | -1546.786820 | -1183.888786 | -1420.639845 | -58599.414344 | -332103.534732 | 9947.790311 | 2468.299414 | 2353.493685 | 2194.301690 | 2095.819953 | 1978.413456 | 1180.396571 | 807.702915 | 968.566946 | 2883.434184 | 2821.521584 | 2824.407374 | 2856.297511 | 2190.191630 | 887.174322 | -509.114724 | -623.469229 | 3402.423794 | 3528.560872 | 4017.044333 | 4610.151119 | 3486.457401 | -2378.475988 | 8359.070364 | -3233.409106 | 4106.970610 | 3201.197494 | 5325.015032 | 9054.715087 | 8435.224996 | -16879.972580 | 5138.919250 | -10241.645350 | 2026.397097 | 2707.983933 | 7715.804121 | 49548.037738 | -16136.273033 | -9072.967137 | -10800.652667 | 39501.240481 | 1249.164948 | 1558.947816 | 9373.244453 | -17437.164612 | -2582.138410 | -28446.655699 | 121570.996895 | 8644.380921 | 8810.528937 | -12.757011 | 15535.137123 | 164332.664281 | 2571.191076 | -271.730325 | 176501.906105 | 6180.641581 | -1204.616507 | 6318.638895 | -736.255448 | -6226.449672 | -1057.136517 | 35015.180776 | 68359.905868 | 5747.898633 | 2663.130313 | 2612.932139 | 2555.487826 | 2680.148636 | 2540.853548 | 1777.169102 | -6744.230283 | -2503.237881 | 3212.512656 | 3317.287711 | 3358.361048 | 4186.227430 | 4675.709195 | 1622.867098 | -18336.087717 | -11776.076779 | 3896.057738 | 2688.395686 | 4152.855027 | 7655.626264 | 14841.603253 | -18287.976380 | -245893.801223 | 31947.368613 | 4687.708805 | 5028.455335 | 5344.359226 | -22848.614930 | -62885.717087 | 15095797.793571 | -585018.530440 | 9397.256019 | 1449.123655 | 1253.313954 | 4416.601905 | -31074.986120 | 1298.997586 | -8590.404152 | -177423.713281 | 6216.843474 | 603.491979 | 1116.378027 | -7607.305222 | -22151.281963 | 9640.042105 | 436.021508 | 6623.429633 | 4900.192121 | -731.411503 | 9049.990746 | -8343.260567 | -199607.660816 | -7440.860609 | -37603.169545 | 304.397482 | 4078.139931 | -4930.170469 | 26319.482569 | 2062.351232 | 895997.468890 | -258559.891890 | 29219.802259 | -24589.348600 | 3819.009819 | 2904.357637 | 2975.726642 | 3021.126379 | 3065.253908 | 3904.419558 | 4538.732809 | -7052.768931 | 6379.818052 | 3628.465353 | 3835.774446 | 3095.523095 | 5724.106092 | 11482.142180 | 19547.447148 | -32510.861225 | 3721.848888 | 4462.975864 | 2081.528721 | 4696.973052 | 4417.742139 | -68015.641319 | -38180.776120 | -10663.656401 | 2571.145720 | 5302.134096 | 1633.055149 | 23395.089024 | 2571.970858 | -149184.606211 | -1166.772309 | 3461.796584 | 2047.658232 | 1242.502856 | 1356.640682 | -123134.921908 | -66642.677331 | -4567.100054 | 161610.044070 | 16637.529556 | 1991.817371 | 615.777730 | 357.966558 | 58194.469817 | -4327.174721 | 38364.136123 | -26911.907541 | 2282.227010 | 2138.422192 | -212.973234 | -486130.190459 | -23776.623549 | -8771.117111 | 30718.575206 | 500027.889141 | 769.590496 | 2287.527945 | -22663.474921 | 286505.189362 | 53027.769392 | -11338.093849 | 34728.775188 | 43494.250491 | 536.900051 | 2414.075449 |
| 1991-05-31 00:00:00 | 1432 | 1523.000000 | 1512.659415 | 1383.624577 | 1281.220072 | 1190.627609 | 1169.951686 | 1217.706435 | 439.014974 | 301.510410 | 1567.099974 | 1380.469688 | 1248.451213 | 1144.777106 | 668.183251 | -61.065477 | -877.213844 | -1518.065102 | 1721.685324 | 1507.877784 | 1358.561360 | 1247.141374 | 1920.662072 | 1133.169117 | -318.187353 | -4222.686094 | 1970.986289 | 1712.178197 | 1074.410008 | 2858.837734 | 9259.852266 | 61983.802720 | -250.051827 | 2744.021750 | 1487.756312 | 296.882198 | -423.297965 | -375.170405 | -4160.934138 | -7576.026867 | -9485.748163 | -21967.166457 | 2241.273454 | 183.537045 | -1770.127939 | -3787.649976 | -9553.085171 | 3586.675813 | 267.448115 | -3674.137156 | 3892.949731 | 1240.165096 | -419.685602 | -418.932197 | -4344.851013 | -8685.822316 | -16731.205070 | 8415.177786 | 6188.278480 | 4222.477654 | 3552.768013 | 7449.655233 | 1745.156017 | -1193.539453 | -5213.153138 | -8273.641490 | 1766.636191 | 1625.011285 | 1465.774481 | 1327.599723 | 1179.537249 | 1200.238211 | 793.658431 | 157.755687 | 1948.419485 | 1780.207043 | 1560.743115 | 1350.948480 | 1538.026507 | 472.155601 | 3324.194533 | 2390.406985 | 2111.119404 | 1357.800076 | 617.390242 | 154.343871 | 141.988960 | 1491.710698 | 12405.276673 | 41535.892148 | 2984.314129 | 1919.157489 | 576.406384 | -663.332742 | -1739.543447 | -2924.973046 | -5250.924596 | -129.530612 | 4174.340515 | 3382.922914 | 1680.803204 | -477.494345 | -3114.850695 | -8865.616206 | -15663.122147 | -8198.737670 | 5287.957154 | 5542.718914 | 4329.607592 | 1487.588680 | -8578.569081 | 2466.620120 | -4290.792140 | -8205.898238 | 5792.781638 | 7669.181777 | 8354.868311 | 8754.779487 | -1838.011723 | 54614.802681 | 1410.474375 | 12677.621766 | 5496.028639 | 8878.877630 | 13774.213497 | 37281.659912 | -8709.983886 | 64095.829739 | 5567.832468 | 2372.734679 | 1969.393786 | 1868.704854 | 1712.248211 | 1468.322069 | 1250.337174 | 1026.377058 | 1690.893605 | 2172.214881 | 2166.797467 | 2032.817106 | 1347.661105 | 771.992539 | 367.438244 | 203.890095 | 603.282344 | 4447.856339 | 2349.049786 | 2234.087285 | 1947.055785 | 986.903438 | 135.255701 | -591.744888 | -1370.142866 | -2278.582612 | 2650.398714 | 4077.005611 | 3471.579007 | 2484.945642 | 1518.199819 | 949.489243 | -283.617299 | -180.693977 | 3007.443174 | 5296.611308 | 5552.545673 | 5369.602270 | -3743.453509 | 5756.899528 | 10137.142392 | -6162.259481 | 3597.267989 | 5801.476126 | 7019.561876 | 8516.771086 | 16527.694482 | 4896.579355 | 5474.711718 | -10753.260972 | 4283.887243 | 5416.790354 | 6539.620256 | -5998.731710 | 4693.720348 | 223077.310637 | -5312.327240 | -90541.403243 | 3544.763345 | 5578.729798 | 4187.983000 | -2929.565626 | 19173.000388 | 3296.111354 | 33206.344668 | 9379.130219 | 2099.890491 | 2055.985704 | 1896.573624 | 1692.862639 | 1400.255744 | 1348.794585 | 1277.693461 | 3075.605336 | 2425.583443 | 2309.850388 | 2322.796050 | 1689.279489 | 1146.800807 | 872.714392 | 1099.595480 | 4032.200015 | 2792.571132 | 2739.619252 | 3472.539629 | 2820.172425 | 2181.845547 | 1908.810834 | 2280.955051 | 6637.079930 | 3302.844346 | 3436.605884 | 3603.852031 | 4278.535338 | 3567.981315 | 2393.086679 | 2491.332092 | 7336.760331 | 4054.311346 | 4419.984084 | 4676.526949 | 5009.068377 | 3664.166365 | 149.054807 | -466.034506 | 4131.197445 | 5040.369231 | 5579.036184 | 7175.969929 | 5199.293473 | -638.604745 | -19595.234796 | 253.018192 | 329.964492 | 3022.519704 | 5626.393970 | 18957.039739 | 11882.344613 | -4085.258249 | 748.824962 | -101783.493526 | -4069.057834 | 2482.054534 | 6212.347642 | -2284.999300 | -1238.366663 | -25519.273738 | -27661.742189 | 122.111922 | -16828.232480 | 2356.244039 | 2291.057133 | 2186.450175 | 2019.667643 | 1805.245382 | 807.546257 | 1346.103645 | 2624.362486 | 2726.211981 | 2752.921085 | 2724.649268 | 2740.113667 | 2418.116611 | 1391.618917 | 1320.516584 | 2623.165148 | 3368.186578 | 3534.290426 | 3784.190376 | 3792.460719 | 3201.816718 | 1310.953359 | 339.161037 | 1858.201792 | 4278.803476 | 4770.641542 | 5204.531021 | 6571.122633 | 3561.933386 | -5139.829917 | -366.104201 | -756.780815 | 5424.559557 | 4440.587150 | 8401.391667 | 19902.296212 | 4971.555276 | -131033.787337 | -12952.510361 | -5064.842632 | 2344.590123 | 4133.392101 | 11726.792613 | 1614.649913 | -9349.177132 | 19258.281921 | -162.154569 | 10884.911288 | 1428.343184 | 3100.923923 | 11727.094771 | 1832.942441 | 12381.682504 | -4323.177262 | 999.661873 | 4019.978557 | 47.715318 | 1197.572824 | 8422.955001 | -1503.039928 | 23744.462928 | 17931.461039 | -70672.832073 | 3409.914803 | 2609.206721 | 2597.650363 | 2522.004100 | 2547.611931 | 2548.820731 | 1447.400444 | 944.380161 | 1137.601098 | 3231.389541 | 3340.668742 | 3613.926615 | 4106.876730 | 3273.845419 | 1387.930317 | -1049.631229 | -1383.037125 | 4090.942602 | 4635.782107 | 5143.915573 | 7025.829899 | 6874.469710 | -6970.596046 | 86712.496801 | -41624.087567 | 5368.086015 | 3566.447623 | 6626.101765 | 14230.126681 | 39124.201778 | -49039.744198 | 6018.285802 | 11394.102926 | 2038.488605 | 2887.103917 | 11639.735994 | 7668.337817 | -7309.873642 | 1167754.846895 | -21441.915327 | 7924.157844 | 1109.231312 | 1517.382064 | 10511.585937 | 14064.532366 | -49302.713063 | 44990.464932 | -35732.428095 | 9450.320024 | 10585.842923 | -521.416747 | 18160.991153 | 285678.924389 | 3901.430063 | 6840.559960 | 362647.163077 | 34803.806353 | -2103.335174 | 10181.635517 | -2264.698292 | 3916.120765 | -13168.109918 | 993.442105 | 429513.756154 | -7957.345900 | 2908.802778 | 2987.228406 | 3064.630101 | 3324.714126 | 3379.878619 | 2457.896549 | -4825.338657 | -7237.174765 | 3762.872752 | 4180.628352 | 4548.429417 | 5635.217367 | 7164.872355 | 2774.737138 | -40831.839104 | 30835.536089 | 4992.824194 | 2891.246891 | 4959.827265 | 10747.205293 | 23972.026682 | -30537.521164 | -1992506.088848 | 14584.637879 | 6547.054125 | 7708.613855 | 6388.417646 | -236687.339498 | -68054.357575 | 224055.664530 | -774238.332291 | 17538.864417 | 1289.597503 | 1027.986194 | 4945.088172 | -47088.495400 | 1136.926885 | 5144.343177 | 138308.142267 | 302575.921440 | 260.092731 | 836.164511 | -13515.478400 | -50270.262460 | -47678.804774 | 37478.500378 | -10158.255381 | -10899.636868 | -1134.566893 | 10784.756688 | -5244.671051 | 11173813.767816 | -18341.245965 | -15849.323944 | -231.143433 | -7355.554543 | -3118.040326 | -6160.826258 | -155319.995491 | 63389.104379 | -524681.696097 | 14291.197707 | -29079.943069 | -12736.732004 | 3300.507954 | 3506.912480 | 3583.018248 | 3647.987648 | 5127.080251 | 5245.424625 | -3177.593220 | -13619.031990 | 4492.821132 | 4928.908300 | 3300.555416 | 7379.139235 | 16903.249196 | 17231.844990 | -3793.847634 | -15312.185701 | 6027.212516 | 1863.624953 | 4818.775386 | 5613.058563 | -74628.230460 | 6815.383730 | -6243.663857 | -7523.916803 | 7488.797608 | 1074.777247 | 20548.532389 | -1968.928755 | -90630.463241 | 76.392815 | -3691.120656 | -4328.716010 | 817.839025 | 52.741161 | -56527.307743 | 10326.822356 | -63828.907698 | -16018.012933 | -96966.929882 | -3473.065913 | -61.133234 | 1184.758689 | -262670.056723 | -5642.050687 | 33095.154869 | 354.262717 | -1166.056677 | -3199.358200 | -882.408717 | -35985.761861 | -131683.758565 | -29724.653112 | 248666.192521 | -1323112.366129 | 3513.253159 | -2905.292714 | -28112.106707 | 57650.799335 | -117039.853232 | 171566.634430 | 61080.688131 | -2786848.843032 | 4646.919423 | -2605.717202 |
| Alpha Values | Beta Values | Gamma Values | Train RMSE | Test RMSE | |
|---|---|---|---|---|---|
| 0 | 0.3 | 0.3 | 0.3 | 393.061188 | 343.618889 |
| 66 | 0.4 | 0.3 | 0.5 | 438.066407 | 412.651659 |
| 131 | 0.5 | 0.3 | 0.6 | 521.672404 | 441.526658 |
| 296 | 0.7 | 0.8 | 0.3 | 700.317756 | 518.188752 |
| 9 | 0.3 | 0.4 | 0.4 | 414.613110 | 579.114027 |
| Test RMSE | |
|---|---|
| Alpha=0.7,Beta=0.3,Gamma=0.3,TripleExponentialSmoothing | 343.618889 |
| Alpha=0.146,Beta=0.053,Gamma=0.393,TripleExponentialSmoothing | 469.656044 |
| 2_point_trailing_Moving_Average | 813.400684 |
| 4_point_trailing_Moving_Average | 1156.589694 |
| SimpleAverageModel | 1275.081804 |
| 6_point_trailing_Moving_Average | 1283.927428 |
| Alpha=0.03,SimpleExponentialSmoothing | 1316.135411 |
| 9_point_trailing_Moving_Average | 1346.278315 |
| RegressionOnTime | 1389.135175 |
| Alpha=0.4,SimpleExponentialSmoothing | 1935.507132 |
| NaiveModel | 3864.279352 |
| Alpha=0.3,Beta=0.3,DoubleExponentialSmoothing | 18259.110704 |
plt.figure(figsize=(18,9))
plt.plot(train["Sparkling"], label="Train")
plt.plot(test["Sparkling"], label="Test")
plt.plot(SES_test["predict"], label="Alpha =0.03 Simple Exponential Smoothing predictions on Test Set")
plt.plot(DES_test["predict", 0.3, 0.3], label="Alpha=0.3,Beta=0.3,DoubleExponentialSmoothing predictions on Test Set")
plt.plot(TES_test["predict", 0.7, 0.3, 0.3], label="Alpha=0.7,Beta=0.3,Gamma=0.3,TripleExponentialSmoothing predictions on Test Set")
plt.legend(loc="best")
plt.grid();
plt.title("Plot of Exponential Smoothing Predictions and the Acutal Values");
plt.show()
fullmodel1 = ExponentialSmoothing(spdf,trend="additive",seasonal="multiplicative")
fullmodel1= fullmodel1.fit(smoothing_level=0.7, smoothing_trend=0.3, smoothing_seasonal=0.3)
RMSE_fullmodel1 = rmse(spdf["Sparkling"], fullmodel1.fittedvalues)
display("RMSE", RMSE_fullmodel1)
prediction_1 = fullmodel1.forecast(steps=len(test))
spdf.plot(legend=True, label="Actual")
prediction_1.plot(legend=True, label="Forecast")
plt.show()
'RMSE'
507.2986253194253
pred_1_df = pd.DataFrame({"lower_CI":prediction_1 - 1.96*fullmodel1.resid.std(),
"prediction":prediction_1,
"upper_ci": prediction_1 + 1.96*fullmodel1.resid.std()})
display(pred_1_df.head().style)
axis = spdf.plot(label="Actual", figsize=(15,8))
pred_1_df["prediction"].plot(ax=axis, label="Forecast", alpha=1) # alpha here is for transparency of the prediction line
axis.fill_between(pred_1_df.index, pred_1_df["lower_CI"], pred_1_df["upper_ci"], color="green", alpha=.15) # alpha here denotes the transparency of the shaded region
axis.set_xlabel("Year-Months")
axis.set_ylabel("Sparkling")
plt.legend(loc="best")
plt.grid()
plt.show();
| lower_CI | prediction | upper_ci | |
|---|---|---|---|
| 1995-08-31 00:00:00 | 997.209090 | 1993.942591 | 2990.676091 |
| 1995-09-30 00:00:00 | 1773.930289 | 2770.663790 | 3767.397290 |
| 1995-10-31 00:00:00 | 2265.505136 | 3262.238636 | 4258.972137 |
| 1995-11-30 00:00:00 | 3040.898303 | 4037.631804 | 5034.365305 |
| 1995-12-31 00:00:00 | 5352.207932 | 6348.941433 | 7345.674933 |
import itertools # library for generating all possible combinations of given number sets
from statsmodels.tsa.arima_model import ARIMA
p = q = range(0, 4)
d= range(1,2) # required as itertools product function expects the parameters as range objects, even if it is only value
pdq = list(itertools.product(p, d, q))
# Creating an empty Dataframe with column names only
ARIMA_AIC = pd.DataFrame(columns=["Param", "AIC"])
ARIMA_AIC
for param in pdq:
ARIMA_model = ARIMA(train["Sparkling"], order=param).fit()
display(f"ARIMA{param} - AIC:{ARIMA_model.aic}")
ARIMA_AIC=ARIMA_AIC.append({"Param":param, "AIC": ARIMA_model.aic}, ignore_index=True)
display(ARIMA_AIC.sort_values(by=["AIC"],ascending=True))
'ARIMA(0, 1, 0) - AIC:2269.582796371201'
'ARIMA(0, 1, 1) - AIC:2264.906438611577'
'ARIMA(0, 1, 2) - AIC:2232.7830976841233'
'ARIMA(0, 1, 3) - AIC:2233.0166051379524'
'ARIMA(1, 1, 0) - AIC:2268.5280606259744'
'ARIMA(1, 1, 1) - AIC:2235.013945349901'
'ARIMA(1, 1, 2) - AIC:2233.5976471190174'
'ARIMA(1, 1, 3) - AIC:2234.5741415463535'
'ARIMA(2, 1, 0) - AIC:2262.035600157607'
'ARIMA(2, 1, 1) - AIC:2232.3604898840485'
C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\base\model.py:547: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available
warnings.warn('Inverting hessian failed, no bse or cov_params '
C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\base\model.py:566: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
warnings.warn("Maximum Likelihood optimization failed to "
'ARIMA(2, 1, 2) - AIC:2210.621173780754'
'ARIMA(2, 1, 3) - AIC:2229.3580937723214'
'ARIMA(3, 1, 0) - AIC:2259.471554711154'
'ARIMA(3, 1, 1) - AIC:2233.921768799295'
'ARIMA(3, 1, 2) - AIC:2228.9282803019664'
C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\base\model.py:547: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available
warnings.warn('Inverting hessian failed, no bse or cov_params '
'ARIMA(3, 1, 3) - AIC:2225.6615585250906'
| Param | AIC | |
|---|---|---|
| 10 | (2, 1, 2) | 2210.621174 |
| 15 | (3, 1, 3) | 2225.661559 |
| 14 | (3, 1, 2) | 2228.928280 |
| 11 | (2, 1, 3) | 2229.358094 |
| 9 | (2, 1, 1) | 2232.360490 |
| 2 | (0, 1, 2) | 2232.783098 |
| 3 | (0, 1, 3) | 2233.016605 |
| 6 | (1, 1, 2) | 2233.597647 |
| 13 | (3, 1, 1) | 2233.921769 |
| 7 | (1, 1, 3) | 2234.574142 |
| 5 | (1, 1, 1) | 2235.013945 |
| 12 | (3, 1, 0) | 2259.471555 |
| 8 | (2, 1, 0) | 2262.035600 |
| 1 | (0, 1, 1) | 2264.906439 |
| 4 | (1, 1, 0) | 2268.528061 |
| 0 | (0, 1, 0) | 2269.582796 |
auto_ARIMA = ARIMA(train["Sparkling"], order=(2,1,2),freq='M')
results_auto_ARIMA = auto_ARIMA.fit()
display(results_auto_ARIMA.summary())
C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\base\model.py:547: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available
warnings.warn('Inverting hessian failed, no bse or cov_params '
C:\ProgramData\Anaconda3\lib\site-packages\statsmodels\base\model.py:566: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
warnings.warn("Maximum Likelihood optimization failed to "
| Dep. Variable: | D.Sparkling | No. Observations: | 131 |
|---|---|---|---|
| Model: | ARIMA(2, 1, 2) | Log Likelihood | -1099.311 |
| Method: | css-mle | S.D. of innovations | 1013.252 |
| Date: | Sun, 15 Aug 2021 | AIC | 2210.621 |
| Time: | 08:41:26 | BIC | 2227.872 |
| Sample: | 02-29-1980 | HQIC | 2217.631 |
| - 12-31-1990 |
| coef | std err | z | P>|z| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| const | 5.5853 | 0.518 | 10.792 | 0.000 | 4.571 | 6.600 |
| ar.L1.D.Sparkling | 1.2699 | 0.075 | 17.043 | 0.000 | 1.124 | 1.416 |
| ar.L2.D.Sparkling | -0.5602 | 0.074 | -7.618 | 0.000 | -0.704 | -0.416 |
| ma.L1.D.Sparkling | -1.9967 | 0.042 | -47.031 | 0.000 | -2.080 | -1.913 |
| ma.L2.D.Sparkling | 0.9967 | 0.043 | 23.432 | 0.000 | 0.913 | 1.080 |
| Real | Imaginary | Modulus | Frequency | |
|---|---|---|---|---|
| AR.1 | 1.1335 | -0.7074j | 1.3361 | -0.0888 |
| AR.2 | 1.1335 | +0.7074j | 1.3361 | 0.0888 |
| MA.1 | 1.0003 | +0.0000j | 1.0003 | 0.0000 |
| MA.2 | 1.0030 | +0.0000j | 1.0030 | 0.0000 |
predicted_auto_ARIMA = results_auto_ARIMA.forecast(steps=len(test))
RMSE_autoarima = rmse(test["Sparkling"],predicted_auto_ARIMA[0])
display(RMSE_autoarima)
resultsDf_arima = pd.DataFrame({'Test RMSE': [RMSE_autoarima]}
,index=['ARIMA(2,1,2)'])
resultsDf = pd.concat([resultsDf, resultsDf_arima])
display(resultsDf)
1374.3117112401214
| Test RMSE | |
|---|---|
| RegressionOnTime | 1389.135175 |
| NaiveModel | 3864.279352 |
| SimpleAverageModel | 1275.081804 |
| 2_point_trailing_Moving_Average | 813.400684 |
| 4_point_trailing_Moving_Average | 1156.589694 |
| 6_point_trailing_Moving_Average | 1283.927428 |
| 9_point_trailing_Moving_Average | 1346.278315 |
| Alpha=0.03,SimpleExponentialSmoothing | 1316.135411 |
| Alpha=0.4,SimpleExponentialSmoothing | 1935.507132 |
| Alpha=0.3,Beta=0.3,DoubleExponentialSmoothing | 18259.110704 |
| Alpha=0.146,Beta=0.053,Gamma=0.393,TripleExponentialSmoothing | 469.656044 |
| Alpha=0.7,Beta=0.3,Gamma=0.3,TripleExponentialSmoothing | 343.618889 |
| ARIMA(2,1,2) | 1374.311711 |
from statsmodels.tsa.stattools import adfuller
display("Results of Dickey-Fuller Test:")
dftest = adfuller(spdf["Sparkling"])
dfoutput = pd.Series(dftest[0:4], index=["Test Statistic","p-value","#Lags Used","Number of Observations Used"])
for key,value in dftest[4].items():
dfoutput["Critical Value (%s)"%key] = value
display(dfoutput)
display("P Value: ", dftest[1], "H0 rejected and the time series is stationary")
'Results of Dickey-Fuller Test:'
Test Statistic -1.360497 p-value 0.601061 #Lags Used 11.000000 Number of Observations Used 175.000000 Critical Value (1%) -3.468280 Critical Value (5%) -2.878202 Critical Value (10%) -2.575653 dtype: float64
'P Value: '
0.6010608871634866
'H0 rejected and the time series is stationary'
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
plot_acf(spdf["Sparkling"].diff().dropna(),lags=50,title='Differenced Data Autocorrelation');
plot_pacf(spdf["Sparkling"].diff().dropna(),lags=50,title='Differenced Data Partial Autocorrelation');
plt.show()
display("p value from PACF: 3 & q value from ACF: 2")
manual_ARIMA = ARIMA(train["Sparkling"].astype("float64"), order=(3,1,2),freq="M")
results_manual_ARIMA = manual_ARIMA.fit()
display(results_manual_ARIMA.summary())
predicted_manual_ARIMA = results_manual_ARIMA.forecast(steps=len(test))
RMSE_manualarima = rmse(test["Sparkling"],
predicted_manual_ARIMA[0])
resultsDf_manual_arima = pd.DataFrame({'Test RMSE': [RMSE_manualarima]}
,index=['Manual ARIMA(3,1,2)'])
resultsDf = pd.concat([resultsDf, resultsDf_manual_arima])
display(resultsDf)
'p value from PACF: 3 & q value from ACF: 2'
| Dep. Variable: | D.Sparkling | No. Observations: | 131 |
|---|---|---|---|
| Model: | ARIMA(3, 1, 2) | Log Likelihood | -1107.464 |
| Method: | css-mle | S.D. of innovations | 1106.327 |
| Date: | Sun, 15 Aug 2021 | AIC | 2228.928 |
| Time: | 08:41:28 | BIC | 2249.055 |
| Sample: | 02-29-1980 | HQIC | 2237.107 |
| - 12-31-1990 |
| coef | std err | z | P>|z| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| const | 5.9574 | 3.643 | 1.635 | 0.102 | -1.184 | 13.099 |
| ar.L1.D.Sparkling | -0.4424 | 2.11e-05 | -2.1e+04 | 0.000 | -0.442 | -0.442 |
| ar.L2.D.Sparkling | 0.3080 | 7.38e-05 | 4171.718 | 0.000 | 0.308 | 0.308 |
| ar.L3.D.Sparkling | -0.2496 | 5.94e-05 | -4205.282 | 0.000 | -0.250 | -0.249 |
| ma.L1.D.Sparkling | -0.0009 | 0.019 | -0.045 | 0.964 | -0.039 | 0.037 |
| ma.L2.D.Sparkling | -0.9991 | 0.019 | -51.796 | 0.000 | -1.037 | -0.961 |
| Real | Imaginary | Modulus | Frequency | |
|---|---|---|---|---|
| AR.1 | -1.0000 | -0.0000j | 1.0000 | -0.5000 |
| AR.2 | 1.1170 | -1.6610j | 2.0017 | -0.1558 |
| AR.3 | 1.1170 | +1.6610j | 2.0017 | 0.1558 |
| MA.1 | 1.0000 | +0.0000j | 1.0000 | 0.0000 |
| MA.2 | -1.0009 | +0.0000j | 1.0009 | 0.5000 |
| Test RMSE | |
|---|---|
| RegressionOnTime | 1389.135175 |
| NaiveModel | 3864.279352 |
| SimpleAverageModel | 1275.081804 |
| 2_point_trailing_Moving_Average | 813.400684 |
| 4_point_trailing_Moving_Average | 1156.589694 |
| 6_point_trailing_Moving_Average | 1283.927428 |
| 9_point_trailing_Moving_Average | 1346.278315 |
| Alpha=0.03,SimpleExponentialSmoothing | 1316.135411 |
| Alpha=0.4,SimpleExponentialSmoothing | 1935.507132 |
| Alpha=0.3,Beta=0.3,DoubleExponentialSmoothing | 18259.110704 |
| Alpha=0.146,Beta=0.053,Gamma=0.393,TripleExponentialSmoothing | 469.656044 |
| Alpha=0.7,Beta=0.3,Gamma=0.3,TripleExponentialSmoothing | 343.618889 |
| ARIMA(2,1,2) | 1374.311711 |
| Manual ARIMA(3,1,2) | 1378.094442 |
plot_acf(spdf["Sparkling"].diff().dropna(),lags=50,title="Differenced Data Autocorrelation");
plt.show()
display("Seasonality is observed for 6 and 12")
'Seasonality is observed for 6 and 12'
from statsmodels.tsa.statespace.sarimax import SARIMAX
p = q = range(0, 3)
d= range(1,2)
D = range(0,1)
pdq = list(itertools.product(p, d, q))
model_pdq = [(x[0], x[1], x[2], 6) for x in list(itertools.product(p, D, q))] # seasonal PDQ
SARIMA_AIC = pd.DataFrame(columns=['param','seasonal', 'AIC'])
for param in pdq:
for param_seasonal in model_pdq:
SARIMA_model = SARIMAX(train["Sparkling"],order=param,
seasonal_order = param_seasonal,enforce_stationarity=False,
enforce_invertibility=False)
results_SARIMA = SARIMA_model.fit(maxiter=1000)
SARIMA_AIC = SARIMA_AIC.append({"param":param,
"seasonal":param_seasonal,
"AIC": results_SARIMA.aic},
ignore_index=True)
SARIMA_AIC.sort_values(by=['AIC']).head()
| param | seasonal | AIC | |
|---|---|---|---|
| 53 | (1, 1, 2) | (2, 0, 2, 6) | 1727.666979 |
| 26 | (0, 1, 2) | (2, 0, 2, 6) | 1727.888803 |
| 80 | (2, 1, 2) | (2, 0, 2, 6) | 1729.153774 |
| 17 | (0, 1, 1) | (2, 0, 2, 6) | 1741.703671 |
| 44 | (1, 1, 1) | (2, 0, 2, 6) | 1743.379778 |
auto_SARIMA_6 = SARIMAX(train["Sparkling"].values,
order=(1,1,2),
seasonal_order=(2,0,2,6),
enforce_stationarity=False,
enforce_ivertibility=False)
results_auto_SARIMA_6 = auto_SARIMA_6.fit(maxiter=1000)
display(results_auto_SARIMA_6.summary())
| Dep. Variable: | y | No. Observations: | 132 |
|---|---|---|---|
| Model: | SARIMAX(1, 1, 2)x(2, 0, 2, 6) | Log Likelihood | -857.437 |
| Date: | Sun, 15 Aug 2021 | AIC | 1730.874 |
| Time: | 08:42:43 | BIC | 1752.902 |
| Sample: | 0 | HQIC | 1739.816 |
| - 132 | |||
| Covariance Type: | opg |
| coef | std err | z | P>|z| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| ar.L1 | -0.6339 | 0.220 | -2.877 | 0.004 | -1.066 | -0.202 |
| ma.L1 | -0.1876 | 0.234 | -0.802 | 0.423 | -0.646 | 0.271 |
| ma.L2 | -0.8123 | 0.171 | -4.747 | 0.000 | -1.148 | -0.477 |
| ar.S.L6 | -0.0170 | 0.033 | -0.510 | 0.610 | -0.082 | 0.048 |
| ar.S.L12 | 1.0230 | 0.021 | 47.746 | 0.000 | 0.981 | 1.065 |
| ma.S.L6 | 0.1487 | 0.167 | 0.892 | 0.373 | -0.178 | 0.475 |
| ma.S.L12 | -0.5516 | 0.111 | -4.974 | 0.000 | -0.769 | -0.334 |
| sigma2 | 1.453e+05 | 1.43e-06 | 1.01e+11 | 0.000 | 1.45e+05 | 1.45e+05 |
| Ljung-Box (L1) (Q): | 0.07 | Jarque-Bera (JB): | 15.49 |
|---|---|---|---|
| Prob(Q): | 0.79 | Prob(JB): | 0.00 |
| Heteroskedasticity (H): | 2.74 | Skew: | 0.41 |
| Prob(H) (two-sided): | 0.00 | Kurtosis: | 4.59 |
predicted_auto_SARIMA_6 = results_auto_SARIMA_6.get_forecast(steps=len(test))
display(predicted_auto_SARIMA_6.summary_frame(alpha=0.05).head())
rmse_autosarima6 = rmse(test["Sparkling"], predicted_auto_SARIMA_6.predicted_mean)
display(rmse_autosarima6)
temp_resultsDf = pd.DataFrame({"Test RMSE" : [rmse_autosarima6]}, index = ["SARIMA(1,1,2)(2,0,2,6)"])
resultsDf = pd.concat([resultsDf, temp_resultsDf])
display(resultsDf)
| y | mean | mean_se | mean_ci_lower | mean_ci_upper |
|---|---|---|---|---|
| 0 | 1550.985488 | 383.019057 | 800.281931 | 2301.689045 |
| 1 | 1418.944299 | 389.744321 | 655.059466 | 2182.829132 |
| 2 | 1894.695343 | 391.659093 | 1127.057626 | 2662.333060 |
| 3 | 1783.949634 | 392.896210 | 1013.887213 | 2554.012055 |
| 4 | 1495.508336 | 393.094407 | 725.057456 | 2265.959216 |
459.6438474254296
| Test RMSE | |
|---|---|
| RegressionOnTime | 1389.135175 |
| NaiveModel | 3864.279352 |
| SimpleAverageModel | 1275.081804 |
| 2_point_trailing_Moving_Average | 813.400684 |
| 4_point_trailing_Moving_Average | 1156.589694 |
| 6_point_trailing_Moving_Average | 1283.927428 |
| 9_point_trailing_Moving_Average | 1346.278315 |
| Alpha=0.03,SimpleExponentialSmoothing | 1316.135411 |
| Alpha=0.4,SimpleExponentialSmoothing | 1935.507132 |
| Alpha=0.3,Beta=0.3,DoubleExponentialSmoothing | 18259.110704 |
| Alpha=0.146,Beta=0.053,Gamma=0.393,TripleExponentialSmoothing | 469.656044 |
| Alpha=0.7,Beta=0.3,Gamma=0.3,TripleExponentialSmoothing | 343.618889 |
| ARIMA(2,1,2) | 1374.311711 |
| Manual ARIMA(3,1,2) | 1378.094442 |
| SARIMA(1,1,2)(2,0,2,6) | 459.643847 |
p = q = range(0, 3)
d= range(1,2)
D = range(0,1)
pdq = list(itertools.product(p, d, q))
model_pdq = [(x[0], x[1], x[2], 12) for x in list(itertools.product(p, D, q))]
SARIMA_AIC = pd.DataFrame(columns=['param','seasonal', 'AIC'])
for param in pdq:
for param_seasonal in model_pdq:
SARIMA_model =SARIMAX(train["Sparkling"],
order=param,
seasonal_order = param_seasonal,
enforce_stationarity=False,
enforce_invertibility=False)
results_SARIMA = SARIMA_model.fit(maxiter=1000)
SARIMA_AIC = SARIMA_AIC.append({"param":param,
"seasonal":param_seasonal,
"AIC": results_SARIMA.aic},
ignore_index=True)
SARIMA_AIC.sort_values(by=["AIC"]).head()
| param | seasonal | AIC | |
|---|---|---|---|
| 50 | (1, 1, 2) | (1, 0, 2, 12) | 1555.584247 |
| 53 | (1, 1, 2) | (2, 0, 2, 12) | 1555.934564 |
| 26 | (0, 1, 2) | (2, 0, 2, 12) | 1557.121574 |
| 23 | (0, 1, 2) | (1, 0, 2, 12) | 1557.160507 |
| 77 | (2, 1, 2) | (1, 0, 2, 12) | 1557.340403 |
auto_SARIMA_12 =SARIMAX(train["Sparkling"],
order=(1, 1, 2),
seasonal_order=(2, 0, 2, 12),
enforce_stationarity=False,
enforce_invertibility=False)
results_auto_SARIMA_12 = auto_SARIMA_12.fit(maxiter=1000)
display(results_auto_SARIMA_12.summary())
| Dep. Variable: | Sparkling | No. Observations: | 132 |
|---|---|---|---|
| Model: | SARIMAX(1, 1, 2)x(2, 0, 2, 12) | Log Likelihood | -769.967 |
| Date: | Sun, 15 Aug 2021 | AIC | 1555.935 |
| Time: | 08:45:30 | BIC | 1577.090 |
| Sample: | 01-31-1980 | HQIC | 1564.505 |
| - 12-31-1990 | |||
| Covariance Type: | opg |
| coef | std err | z | P>|z| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| ar.L1 | -0.6379 | 0.287 | -2.225 | 0.026 | -1.200 | -0.076 |
| ma.L1 | -0.3050 | 0.185 | -1.645 | 0.100 | -0.668 | 0.058 |
| ma.L2 | -0.8913 | 0.275 | -3.246 | 0.001 | -1.430 | -0.353 |
| ar.S.L12 | 0.7612 | 0.567 | 1.343 | 0.179 | -0.350 | 1.872 |
| ar.S.L24 | 0.2951 | 0.590 | 0.500 | 0.617 | -0.861 | 1.451 |
| ma.S.L12 | 1.8831 | 3.334 | 0.565 | 0.572 | -4.652 | 8.418 |
| ma.S.L24 | -1.8033 | 2.473 | -0.729 | 0.466 | -6.650 | 3.044 |
| sigma2 | 1.858e+04 | 4.87e+04 | 0.382 | 0.703 | -7.68e+04 | 1.14e+05 |
| Ljung-Box (L1) (Q): | 0.08 | Jarque-Bera (JB): | 12.53 |
|---|---|---|---|
| Prob(Q): | 0.78 | Prob(JB): | 0.00 |
| Heteroskedasticity (H): | 1.55 | Skew: | 0.35 |
| Prob(H) (two-sided): | 0.20 | Kurtosis: | 4.55 |
predicted_auto_SARIMA_12 = results_auto_SARIMA_12.get_forecast(steps=len(test))
display(predicted_auto_SARIMA_12.summary_frame(alpha=0.05).head())
rmse_autosarima12 = rmse(test["Sparkling"], predicted_auto_SARIMA_12.predicted_mean)
display("RMSE", rmse_autosarima12)
temp_resultsDf = pd.DataFrame({"Test RMSE": [rmse_autosarima12]}, index=['SARIMA(1,1,2)(2,0,2,12)'])
resultsDf = pd.concat([resultsDf, temp_resultsDf])
display(resultsDf)
| Sparkling | mean | mean_se | mean_ci_lower | mean_ci_upper |
|---|---|---|---|---|
| 1991-01-31 | 1317.828231 | 390.273454 | 552.906317 | 2082.750145 |
| 1991-02-28 | 1309.836183 | 403.642457 | 518.711506 | 2100.960861 |
| 1991-03-31 | 1608.903225 | 403.654490 | 817.754963 | 2400.051487 |
| 1991-04-30 | 1599.958000 | 409.154820 | 798.029290 | 2401.886711 |
| 1991-05-31 | 1378.333655 | 410.005730 | 574.737190 | 2181.930120 |
'RMSE'
546.4493980820665
| Test RMSE | |
|---|---|
| RegressionOnTime | 1389.135175 |
| NaiveModel | 3864.279352 |
| SimpleAverageModel | 1275.081804 |
| 2_point_trailing_Moving_Average | 813.400684 |
| 4_point_trailing_Moving_Average | 1156.589694 |
| 6_point_trailing_Moving_Average | 1283.927428 |
| 9_point_trailing_Moving_Average | 1346.278315 |
| Alpha=0.03,SimpleExponentialSmoothing | 1316.135411 |
| Alpha=0.4,SimpleExponentialSmoothing | 1935.507132 |
| Alpha=0.3,Beta=0.3,DoubleExponentialSmoothing | 18259.110704 |
| Alpha=0.146,Beta=0.053,Gamma=0.393,TripleExponentialSmoothing | 469.656044 |
| Alpha=0.7,Beta=0.3,Gamma=0.3,TripleExponentialSmoothing | 343.618889 |
| ARIMA(2,1,2) | 1374.311711 |
| Manual ARIMA(3,1,2) | 1378.094442 |
| SARIMA(1,1,2)(2,0,2,6) | 459.643847 |
| SARIMA(1,1,2)(2,0,2,12) | 546.449398 |
plot_acf(spdf["Sparkling"].diff().dropna(), lags=50, title="Differenced Data Autocorrelation")
plot_pacf(spdf["Sparkling"].diff().dropna(), lags=50, title="Differenced Data Partial Autocorrelation")
plt.show()
spdf.plot()
plt.grid()
plt.show()
(spdf["Sparkling"].diff(6)).plot()
plt.grid()
plt.show()
We see that there might be a slight trend which can be noticed in the data. So we take a differencing of first order on the seasonally differenced series.
(spdf["Sparkling"].diff(6)).diff().plot()
plt.grid()
plt.show()
check the stationarity of the above series before fitting the SARIMA model.
adfuller(train["Sparkling"])[1]
0.6697444263523349
# adfuller((train["Sparkling"].diff(6).dropna()).diff(1).dropna())[1]
Checking the ACF and the PACF plots for the new modified Time Series.
# plot_acf((spdf["Sparkling"].diff(6).dropna()).diff(1).dropna(), lags=30)
# plot_pacf((spdf["Sparkling"].diff(6).dropna()).diff(1).dropna(), lags=30)
# plt.show()
Here, we have taken alpha=0.05.
We are going to take the seasonal period as 6. We will keep the p(0) and q(0) parameters same as the ARIMA model.
The Auto-Regressive parameter in an SARIMA model is 'P' which comes from the significant lag after which the PACF plot cuts-off to 2. The Moving-Average parameter in an SARIMA model is 'Q' which comes from the significant lag after which the ACF plot cuts-off to 2.
manual_SARIMA_6 = SARIMAX(train["Sparkling"],
order=(3,1,2),
seasonal_order=(3,1,2,6),
enforce_stationarity=False,
enforce_invertibility=False)
results_manual_SARIMA_6 = manual_SARIMA_6.fit(maxiter=1000)
display(results_manual_SARIMA_6.summary())
| Dep. Variable: | Sparkling | No. Observations: | 132 |
|---|---|---|---|
| Model: | SARIMAX(3, 1, 2)x(3, 1, 2, 6) | Log Likelihood | -771.745 |
| Date: | Sun, 15 Aug 2021 | AIC | 1565.490 |
| Time: | 08:45:51 | BIC | 1594.578 |
| Sample: | 01-31-1980 | HQIC | 1577.274 |
| - 12-31-1990 | |||
| Covariance Type: | opg |
| coef | std err | z | P>|z| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| ar.L1 | 0.6107 | 0.335 | 1.825 | 0.068 | -0.045 | 1.267 |
| ar.L2 | -0.1817 | 0.176 | -1.035 | 0.301 | -0.526 | 0.163 |
| ar.L3 | 0.0260 | 0.218 | 0.119 | 0.905 | -0.401 | 0.453 |
| ma.L1 | -2.2875 | 0.471 | -4.856 | 0.000 | -3.211 | -1.364 |
| ma.L2 | 1.1623 | 0.538 | 2.159 | 0.031 | 0.107 | 2.217 |
| ar.S.L6 | -1.3086 | 0.277 | -4.725 | 0.000 | -1.851 | -0.766 |
| ar.S.L12 | -0.4371 | 0.401 | -1.091 | 0.275 | -1.223 | 0.348 |
| ar.S.L18 | -0.1499 | 0.213 | -0.704 | 0.481 | -0.567 | 0.267 |
| ma.S.L6 | 0.7332 | 0.395 | 1.858 | 0.063 | -0.040 | 1.507 |
| ma.S.L12 | -0.6079 | 0.298 | -2.039 | 0.041 | -1.192 | -0.024 |
| sigma2 | 4.582e+04 | 1.8e-05 | 2.55e+09 | 0.000 | 4.58e+04 | 4.58e+04 |
| Ljung-Box (L1) (Q): | 0.00 | Jarque-Bera (JB): | 35.42 |
|---|---|---|---|
| Prob(Q): | 0.97 | Prob(JB): | 0.00 |
| Heteroskedasticity (H): | 1.31 | Skew: | 0.56 |
| Prob(H) (two-sided): | 0.42 | Kurtosis: | 5.63 |
manual_SARIMA_12 = SARIMAX(train["Sparkling"],
order=(3,1,2),
seasonal_order=(3,1,2,12),
enforce_stationarity=False,
enforce_invertibility=False)
results_manual_SARIMA_12 = manual_SARIMA_12.fit(maxiter=1000)
display(results_manual_SARIMA_12.summary())
| Dep. Variable: | Sparkling | No. Observations: | 132 |
|---|---|---|---|
| Model: | SARIMAX(3, 1, 2)x(3, 1, 2, 12) | Log Likelihood | -598.630 |
| Date: | Sun, 15 Aug 2021 | AIC | 1219.260 |
| Time: | 08:46:01 | BIC | 1245.462 |
| Sample: | 01-31-1980 | HQIC | 1229.765 |
| - 12-31-1990 | |||
| Covariance Type: | opg |
| coef | std err | z | P>|z| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| ar.L1 | -0.7556 | 0.151 | -5.013 | 0.000 | -1.051 | -0.460 |
| ar.L2 | 0.1169 | 0.185 | 0.633 | 0.527 | -0.245 | 0.479 |
| ar.L3 | -0.0520 | 0.143 | -0.365 | 0.715 | -0.332 | 0.228 |
| ma.L1 | 0.0330 | 0.191 | 0.173 | 0.863 | -0.341 | 0.407 |
| ma.L2 | -0.9670 | 0.156 | -6.197 | 0.000 | -1.273 | -0.661 |
| ar.S.L12 | -0.7538 | 0.496 | -1.520 | 0.128 | -1.725 | 0.218 |
| ar.S.L24 | -0.6371 | 0.351 | -1.818 | 0.069 | -1.324 | 0.050 |
| ar.S.L36 | -0.2469 | 0.151 | -1.641 | 0.101 | -0.542 | 0.048 |
| ma.S.L12 | 0.3719 | 0.491 | 0.758 | 0.448 | -0.590 | 1.334 |
| ma.S.L24 | 0.3466 | 0.365 | 0.949 | 0.343 | -0.370 | 1.063 |
| sigma2 | 1.79e+05 | 1.67e-06 | 1.07e+11 | 0.000 | 1.79e+05 | 1.79e+05 |
| Ljung-Box (L1) (Q): | 0.01 | Jarque-Bera (JB): | 13.16 |
|---|---|---|---|
| Prob(Q): | 0.93 | Prob(JB): | 0.00 |
| Heteroskedasticity (H): | 0.66 | Skew: | 0.62 |
| Prob(H) (two-sided): | 0.29 | Kurtosis: | 4.55 |
predicted_manual_SARIMA_6 = results_manual_SARIMA_6.get_forecast(steps=len(test))
display(predicted_manual_SARIMA_6.summary_frame(alpha=0.05).head())
rmse_manualsarima6 = rmse(test["Sparkling"], predicted_manual_SARIMA_6.predicted_mean)
display(rmse_manualsarima6)
temp_resultsDf = pd.DataFrame({"Test RMSE": [rmse_manualsarima6]}, index=["SARIMA(3,1,2)(3,1,2,6)"])
resultsDf = pd.concat([resultsDf, temp_resultsDf])
predicted_manual_SARIMA_12 = results_manual_SARIMA_12.get_forecast(steps=len(test))
display(predicted_manual_SARIMA_12.summary_frame(alpha=0.05).head())
rmse_manualsarima12 = rmse(test["Sparkling"], predicted_manual_SARIMA_12.predicted_mean)
display(rmse_manualsarima12)
temp_resultsDf = pd.DataFrame({"Test RMSE": [rmse_manualsarima12]}, index=["SARIMA(3,1,2)(3,1,2,12)"])
resultsDf = pd.concat([resultsDf, temp_resultsDf])
| Sparkling | mean | mean_se | mean_ci_lower | mean_ci_upper |
|---|---|---|---|---|
| 1991-01-31 | 1398.425054 | 401.129046 | 612.226571 | 2184.623537 |
| 1991-02-28 | 1071.354225 | 408.565983 | 270.579614 | 1872.128836 |
| 1991-03-31 | 1677.473632 | 408.628746 | 876.576007 | 2478.371257 |
| 1991-04-30 | 1452.893987 | 410.019510 | 649.270514 | 2256.517459 |
| 1991-05-31 | 1145.412195 | 413.586091 | 334.798352 | 1956.026038 |
933.0055860065444
| Sparkling | mean | mean_se | mean_ci_lower | mean_ci_upper |
|---|---|---|---|---|
| 1991-01-31 | 1510.231997 | 425.098757 | 677.053744 | 2343.410250 |
| 1991-02-28 | 1431.674887 | 440.080823 | 569.132324 | 2294.217449 |
| 1991-03-31 | 1850.401507 | 440.152620 | 987.718225 | 2713.084789 |
| 1991-04-30 | 1781.971278 | 440.897834 | 917.827402 | 2646.115155 |
| 1991-05-31 | 1550.443568 | 440.888036 | 686.318897 | 2414.568239 |
329.5350922346566
display(resultsDf.sort_values(by=["Test RMSE"],ascending=True))
| Test RMSE | |
|---|---|
| SARIMA(3,1,2)(3,1,2,12) | 329.535092 |
| Alpha=0.7,Beta=0.3,Gamma=0.3,TripleExponentialSmoothing | 343.618889 |
| SARIMA(1,1,2)(2,0,2,6) | 459.643847 |
| Alpha=0.146,Beta=0.053,Gamma=0.393,TripleExponentialSmoothing | 469.656044 |
| SARIMA(1,1,2)(2,0,2,12) | 546.449398 |
| 2_point_trailing_Moving_Average | 813.400684 |
| SARIMA(3,1,2)(3,1,2,6) | 933.005586 |
| 4_point_trailing_Moving_Average | 1156.589694 |
| SimpleAverageModel | 1275.081804 |
| 6_point_trailing_Moving_Average | 1283.927428 |
| Alpha=0.03,SimpleExponentialSmoothing | 1316.135411 |
| 9_point_trailing_Moving_Average | 1346.278315 |
| ARIMA(2,1,2) | 1374.311711 |
| Manual ARIMA(3,1,2) | 1378.094442 |
| RegressionOnTime | 1389.135175 |
| Alpha=0.4,SimpleExponentialSmoothing | 1935.507132 |
| NaiveModel | 3864.279352 |
| Alpha=0.3,Beta=0.3,DoubleExponentialSmoothing | 18259.110704 |
res_df = pd.DataFrame({'columns': resultsDf.index, 'Test RMSE': resultsDf["Test RMSE"]})
sorted_resDf_values = res_df.sort_values('Test RMSE', ascending=True)
plt.figure(figsize=(10,10))
sns.barplot(x='Test RMSE', y='columns', data=sorted_resDf_values)
plt.xlabel('Test RMSE for all models')
plt.ylabel('Model')
plt.title('Best Models')
plt.show()
full_data_model = SARIMAX(spdf["Sparkling"], order=(3,1,2), seasonal_order=(3,1,2,12),
enforce_stationarity=False,
enforce_invertibility=False)
results_full_data_model = full_data_model.fit(maxiter=1000)
display(results_full_data_model.summary())
| Dep. Variable: | Sparkling | No. Observations: | 187 |
|---|---|---|---|
| Model: | SARIMAX(3, 1, 2)x(3, 1, 2, 12) | Log Likelihood | -1000.243 |
| Date: | Sun, 15 Aug 2021 | AIC | 2022.487 |
| Time: | 08:46:23 | BIC | 2054.445 |
| Sample: | 01-31-1980 | HQIC | 2035.473 |
| - 07-31-1995 | |||
| Covariance Type: | opg |
| coef | std err | z | P>|z| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| ar.L1 | -0.8611 | 0.090 | -9.545 | 0.000 | -1.038 | -0.684 |
| ar.L2 | 0.0118 | 0.129 | 0.091 | 0.927 | -0.242 | 0.265 |
| ar.L3 | -0.0767 | 0.102 | -0.754 | 0.451 | -0.276 | 0.123 |
| ma.L1 | 0.0322 | 0.120 | 0.269 | 0.788 | -0.203 | 0.267 |
| ma.L2 | -0.9678 | 0.098 | -9.838 | 0.000 | -1.161 | -0.775 |
| ar.S.L12 | -0.6102 | 0.392 | -1.556 | 0.120 | -1.379 | 0.159 |
| ar.S.L24 | -0.4984 | 0.231 | -2.162 | 0.031 | -0.950 | -0.047 |
| ar.S.L36 | -0.2472 | 0.109 | -2.263 | 0.024 | -0.461 | -0.033 |
| ma.S.L12 | 0.1230 | 0.395 | 0.311 | 0.756 | -0.652 | 0.898 |
| ma.S.L24 | 0.2492 | 0.266 | 0.937 | 0.349 | -0.272 | 0.770 |
| sigma2 | 1.562e+05 | 1.31e-06 | 1.19e+11 | 0.000 | 1.56e+05 | 1.56e+05 |
| Ljung-Box (L1) (Q): | 0.01 | Jarque-Bera (JB): | 26.96 |
|---|---|---|---|
| Prob(Q): | 0.92 | Prob(JB): | 0.00 |
| Heteroskedasticity (H): | 0.56 | Skew: | 0.59 |
| Prob(H) (two-sided): | 0.05 | Kurtosis: | 4.84 |
predicted_manual_SARIMA_12_full_data = results_full_data_model.get_forecast(steps=12)
display(predicted_manual_SARIMA_12_full_data.summary_frame(alpha=0.05).head())
rmse_full_data = rmse(spdf["Sparkling"], results_full_data_model.fittedvalues)
display(rmse_full_data)
| Sparkling | mean | mean_se | mean_ci_lower | mean_ci_upper |
|---|---|---|---|---|
| 1995-08-31 | 1868.826455 | 396.504223 | 1091.692458 | 2645.960452 |
| 1995-09-30 | 2511.292655 | 401.856913 | 1723.667578 | 3298.917731 |
| 1995-10-31 | 3272.713048 | 402.702600 | 2483.430456 | 4061.995640 |
| 1995-11-30 | 3874.518132 | 403.117621 | 3084.422113 | 4664.614151 |
| 1995-12-31 | 6099.043204 | 403.137241 | 5308.908729 | 6889.177678 |
578.956975049657
pred_full_manual_SARIMA_data = predicted_manual_SARIMA_12_full_data.summary_frame(alpha=0.05).set_index(pd.date_range(start="1995-08-31", end="1996-07-31", freq="M"))
axis = spdf["Sparkling"].plot(label="Observed")
pred_full_manual_SARIMA_data["mean"].plot(ax=axis, label="Forecast", alpha=0.7)
axis.fill_between(pred_full_manual_SARIMA_data.index,
pred_full_manual_SARIMA_data["mean_ci_lower"],
pred_full_manual_SARIMA_data["mean_ci_upper"],
color="green",
alpha=0.15)
axis.set_xlabel("Year-Months")
axis.set_ylabel("Sparkling")
plt.title("Prediction for future 12 months")
plt.legend(loc="best")
plt.show()